Pre-heat oven to 400°.
Line a rimmed baking sheet with parchment paper. In a small bowl, toss bell peppers and baby carrots in 1 tablespoon olive oil until thoroughly coated. Add salt and pepper to taste.
Place bell peppers in a single layer on the prepared cookie sheet and put in the oven for 15 minutes or until the vegetables are cooked through and lightly browned.
While the vegetables are roasting, bring a large salted pot of water to boil and cook pasta according to the package directions.
While the noodles are cooking, heat 2 tablespoons olive oil in a large pan over medium-high heat. Add the garlic, tomatoes, and salt and pepper to taste. Cook the tomatoes for until they begin to blister, about 2 minutes. Turn off the heat, gently toss the tomatoes, and then let sit for 2-3 minutes.
Add cooked pasta and roasted vegetables to your tomato and garlic sauce. Stir gently as to not break up the blistered tomatoes.
Pour pasta in a large serving bowl and sprinkle the basil and Parmesan cheese on top.