Preheat the oven to 475 degrees F (245 degrees C).
Toss bell peppers and fennel with oil and thyme. Place vegetables on a baking sheet.
Roast in the preheated oven until tender, 8 to 10 minutes.
Meanwhile, heat a large skillet over medium-high heat. Add sausage and shallot; saute until sausage is browned and crumbly, 5 to 7 minutes. Drain and discard grease.
Fill a large pot with lightly salted water and bring to a rolling boil. Stir in orecchiette and return to a boil. Cook pasta uncovered, stirring occasionally, until tender yet firm to the bite, 12 to 14 minutes. Drain, reserving 1 cup of the pasta water.
Add orecchiette pasta, tomato paste, garlic, and roasted vegetables to the sausage in the skillet. Cook over medium heat until fragrant, 2 to 3 minutes. Pour in the reserved pasta water; simmer until sauce is reduced to your liking, 3 to 5 minutes more. Remove from heat and stir in basil before serving.