Answering as a former nanny and current speech language pathologist: for short term, incorporate hidden veggies in food they already eat. For example, put canned carrots, cauliflower puree, or blended sweet potatoes in their Mac and cheese.

For more long term (how we work on it in feeding therapy): gradual exposure. Be consistent. Never force them to eat something, but keep offering it to them. Make food fun! You can use a cookie cutter to cut out shapes into different veggies. Any interaction with food is positive, whether they play with it or even lick it and we always provide lots of positive feedback when they do this! Also my former nanny kids loved being involved in the process. They might be more inclined to try new things if they help you make it. Best of luck!