In a soup pot, heat olive oil over medium heat until shimmering. Add sausage and cook until browned, 6 to 8 minutes. Remove and set aside, adjusting fat if necessary.
Add onion, garlic, celery, carrot, fennel, fennel seeds, and crushed red pepper flakes, cooking until softened, about 8 minutes.
Add tomato paste, coating vegetables, and cook until paste is dark red, about 3 minutes. Sprinkle flour and cook until coated, about 2 minutes.
Slowly pour in stock, stirring until flour is incorporated. Bring to a boil, add kale and sausage, and simmer until kale is tender, 8 to 10 minutes.
Cook tortellini in salted water until just shy of al dente, drain and set aside.
Remove soup from heat, stir in heavy cream and tortellini, and season with salt and pepper.
Serve immediately topped with pesto and Parmigiano-Reggiano, if desired.