Bring a large pot of salted water to a boil. Add the rotini and cook until al dente, according to the box directions. Save a cup of the pasta water and drain the rest.
At this point, scoop out two cups of the cooked pasta and place it back in the pot. Add 1/4 cup chicken stock and 1 tablespoon butter. If needed, add a little bit of the reserved pasta water to create a thin sauce. Add 1/4 cup Parmesan and stir to combine.
Serve to your kids as is, or with 1/4 cup warmed peas, with extra grated Parmesan on top.
Place the remaining cooked pasta back in the pot.
In the meantime, heat the oil in a large saute pan over medium-high heat. Add the broccoli florets and asparagus pieces to the pan. Add 1/4 cup water and cover to steam, about 3 minutes.
To the pan, add the cherry tomatoes, white wine, garlic, thyme leaves, 2 tablespoons butter and the remaining 1/2 cup chicken stock. Sprinkle with salt and pepper. Let saute for a few more minutes until the colors pop. Finally, add the peas and toss. Off the heat, add the last tablespoon of butter and another 1/3 cup Parmesan. If needed, stir in a little of the reserved pasta water to create a sauce. Toss to combine.
Serve the adult-friendly pasta primavera with fresh parsley and more Parmesan-and that extra white wine, for Pete's sake!