Bring a large pot of salted water to a boil.
Add the rotini to the boiling water and cook until just tender, about 11 minutes.
Drain the pasta, reserving 3/4 cup of the cooking water, and set it aside.
In a large skillet over medium-high heat, melt the butter and add the olive oil.
Add the onion and cook, stirring, for 2 minutes until it softens.
Add the garlic and cook, stirring, for 30 seconds.
Stir in the broccoli, bell peppers, and carrots.
Cook until the vegetables are slightly tender, about 5-7 minutes.
Pour in the chicken broth and heavy cream.
Bring to a simmer, then stir in the Parmesan cheese.
Season with salt and pepper.
Add the reserved pasta water, cooked pasta, and cherry tomatoes to the pan.
Toss everything together to coat the pasta and vegetables evenly. Garnish with fresh basil before serving.