I sit my kids down to eat before everything is on the table, and bring out of the kitchen and plate for them what I want them to eat -- whether it's something new, veggies, etc. Then in the 5-10 minutes where we get drinks, bring out the rest of the food and serve it, they've typically eaten 50+% of whatever I first served. They're somewhat hungry and haven't snacked and will naturally graze at what's in front of them to pass that time. Then, as you mention, because they've tried it and not found it horrible they'll usually eat the rest of it along with the rest of the food. Soft power in action -- nothing forced, but guiding the activities such that you preferentially select for the outcome that you want.
Not rocket science. Does it work every time? No. Did it work right away? No. But we formed a habit, and we're good now. It works the vast majority of the time, and they eat great elsewhere as a result. When we go out to eat or go to school, they're used to eating all of those things, so they do tend to eat a good chunk of their carrots, peas, etc. and if they don't then oh well -- they eat healthy at home, what's one meal? It's not worth fighting over in those instances since you've already won in the vast majority of the cases.