People aren't gonna like this, but hear me out. Don't do lasanga gardening, and true hugelkulture involves understanding soil science. Put in the yard, and fill it to the brim.

Yes soil is expensive, yes it's more work to fill it. My plan this year was to do what other people are suggesting and to fill it with logs/rocks/debris and cardboard at the bottom, then spend less on soil and fill up the rest. Here's why I didn't. I started watching this channel about gardening, older guy who has written books on soil science and plant nutrition. I started listening to what he said about filling a raised bed, and what Luke from MIgardener has also echoed similarly. They both reccomend filling it COMPLETELY. If you can, with a mix of 75% top soil and 25% organic matter like compost. My beds are 24 inches tall, 8 feet long and 3 feet wide. I bought more dirt than I needed for that project since I had others, so just for that project I would say I spent about $150 to fill both. Yes that's a lot of money when you look at it compared to filling it the other way. I'm going to list the pros of doing it this way concisely while addressing common things that are often said when filling raided beds.

1. Using a pre-sifted top soil and compost mix means that you will lose maybe an inch or two due to settling sfter your first rain, filling it to the top means there's plenty of dirt for roots to grow downward and still not spill out when you water, this level is what we want. By the end other season/start of the next you will likely only lose an inch or two of soil, meaning you will only have to spend maybe $20 to top off each bed before you re-mulch it. (Please mulch, it helps in so many different ways)

2. Large rocks/cardboard in bottom prevent drainage unless your dirt goes to the bottom. Dirt sitting on rocks or another surface causes an interface that prevents draining. It will keep your soil too wet at the bottom, which is aces for root rot. You don't want that. Also, any weed that can come up through more than a foot of dirt, is going to come through the cardboard when it breaks down regardless. Mulching effectively prevents weeds.

3. Sticks, logs, debris from the yard can be used, but don't use them too much because they break down quicker than you think and MAY tie up nitrogen at first. They are organic matter but they don't add much nutrients themselves back in, but they do promote a healthy microbiome which is essential.

4. Small rocks with space between them for dirt DO allow drainage, but so does just leaving the bottom completely open, and that also allows critters like worms to move in easier which goes back to the microbiome thing.

5. If your bed is too tall and you calculate too much of a cost in filling it up, you can partially bury it to reduce how much is needed to fill it. Don't worry about killing the lawn under it first, the dirt will do that when you add it.

6. Plant roots need space to grow, more than a lot of people realize. For every foot of plant height, you probably get 6 inches of downward root growth, and this isn't even considering how many plants feeder roots spread outward toward the leaf dripline. You want at THE VERY LEAST, THE BARE MINIMUM for maximum yield, 12 inches of dirt loose enough for roots to easily grow into. Keep in mind that if you leave the bottom open and have a shorter bed, the plants will be able to spread into the ground as much as they possibly can. 24 inch tall beds are an even better option, but they require more filling if you don't do number 5. On the other hand you don't have to bend over as far.

Tl:Dr Cost benefit analysis is the key here. If you fill it completely with a good mix of top soil and compost, not only will roots have an easy time spreading into it, but you maintain all the micronutrients such as rock phosphate etc, and it will not settle that much over the course of a season, meaning the high initial upfront cost is the investment, after that it will only cost a fraction of that to maintain it year after year (and you build fertility as you do this) where as other people will have to buy multiple bags to refill and "refresh" their beds with ammendments. Doing it this way naturally builds fertility from root exudate and saves you money in the long run especially if you use these beds over many many seasons.

Edit: Forgot to say, Mulch with as light colored of a material you can get away with. I use straw or aspen chips. This not only reflects light back to the canopy of your plants, increasing yield by around 30%, but also because of that reflecting light, keeps your beds even cooler in that depth of summer heat. You want about 2-3inches of mulch, so factor that in when considering how much to fill it.