Bring a large pot of salted water to a boil. Cook the tortellini according to package directions (about 3–4 minutes for fresh or 7–9 minutes for frozen) until tender.
While the tortellini cooks, heat the olive oil and butter in a large skillet over medium heat. Add the minced garlic and sauté for about 30 seconds, just until fragrant.
Stir in the tomato sauce and tomato paste until smooth, then pour in the broth. Add Italian seasoning and (if using) red pepper flakes.
Simmer the sauce for 5–7 minutes, stirring occasionally, until slightly thickened. Reduce heat to low and slowly stir in the heavy cream until fully combined.
Taste the sauce and season with salt and black pepper. If the sauce tastes too sharp, stir in a small pinch of sugar and taste again.
Before draining the pasta, reserve about 1/2 cup of pasta water. Drain the tortellini well.
Add the tortellini to the skillet and gently toss to coat in the sauce. If it seems too thick, add a splash of reserved pasta water until the sauce looks silky and coats the pasta.
Remove from heat and stir in the grated Parmesan. Finish with fresh basil and serve immediately with extra Parmesan on the side.