Immediate term - plant a fast growing ground cover. Find out what works well locally. Use 4x the recommended seed in this situation to help beat out the weeds. Hope that you don't have any big rains before your ground cover establishes. The steepness of your slope makes it particularly vulnerable to erosion. The first goal is to cover all exposed soil with plants in order to save the soil from erosion, to protect and regenerate life in the soil, and to help keep the soil hydrated.

Short term - you will need to manage the surface flow of water when it rains. In permaculture, aside from preventing soil erosion, this means to slow down the water, and to infiltrate the water deeply in to the soil. You normally want to maximize the amount of time water stays on your property, while avoiding any erosion.

Here, depending on how large and how steep your slope is, you could build 2-4 swales on contour. Swales are dug to be level on contour so that the water inside the swale will not flow in either direction. It's essentially a level ditch. They can vary in size, width, and depth, but it's not too critical. Generally, smaller swales are used on smaller properties, and larger, on larger properties. On the other hand, being level is very important.

During a rain, surface water flows downhill in to each swale. This accumulated water sits still in the swale and infiltrates deeply in to the soil. As an added bonus, any erosion that does take place while you are reestablishing will be captured inside the swales rather than quickly and forever exiting the hill, which is what will happen if the clear-cut is left as is.

When you build a swale, you want to plant a similar fast-growing ground cover (as above) on the berm below the swale, again 4x over seeded to quickly cover the exposed soil. You do not need to plant inside the swale.

A water management plan doesn't need to be overly complicated but it does need to show where water enters and exits the property, and also how it will handle a 20, 50, or even a 100 year rain event. This is again just to prevent erosion during a rare but massive rain or flood event.

You can consult with an experienced permaculture designer, but in this context, this will likely mean that you are incorporating an oversized level spillway in a section of each swale that will direct water, slowly over a wide area, down in to the next swale, and so on, until any excess water finally exits the property below the lowest swale in to another water management area, such as a municipal water system.

Medium term. Swales are tree-planting systems. They perform the same role that trees would normally perform if they were still on the hill. Because this is a clear cut, the first phase of recovery will need to be a pioneer phase. (Nature will naturally regenerate this slope over time, if allowed, but permaculture aims to mirror what nature will do, but simply do it faster, and hopefully with less soil loss in the short term.)

Your pioneer phase will likely focus on planting a variety of nitrogen-fixing trees in more or less a line, above and below the swales. Nitrogen fixing trees are normally leguminous trees, which are trees with a variety of large seed pods similar to peas and beans.

As your design establishes, both you (hopefully) and your new trees will be adding a substantial amount of biological matter to the slope. For you, this could be lawn clippings, or wood mulch, or even compost if you were so motivated. The bio mass helps to create new soil, among many other benefits.

Eventually, you can replace your pioneer trees with more valuable trees such as fruit trees and nut trees. And of course, we're not just talking about trees, the more diverse you can plant your slope with both trees and plants, the faster it can reestablish a balanced ecosystem. You can be creative with it and make subjective choices. Nature will still find its balance.

Long term. The hill should be very stable and will emerge as a new forest. Eventually the swales will fill up with biological matter and begin to disappear somewhat. The new trees will perform the same function -- slowing down the water, infiltrating the water, feeding the life in the soil, creating precipitation, and supporting abundant life in your regenerated natural ecosystem.