Brown the Sausage: Heat 2 tablespoons olive oil in a large stockpot over medium heat until shimmering. Add kielbasa and cook slowly, stirring occasionally, until golden and crisp on the edges (6–8 minutes). Remove to a paper towel-lined plate.
Sauté Aromatics: Add remaining olive oil and butter to the pot. Once melted and shimmering, add onion, garlic, carrots, and celery. Season with salt, black pepper, red pepper flakes, thyme, and smoked paprika. Cook, stirring often, until softened but not browned, about 6–7 minutes.
Build the Flavor Base: Stir in the tomato paste and cook 1–2 minutes, letting it darken slightly. Pour in the white wine to deglaze, scraping up the browned bits from the bottom of the pot.
Simmer the Broth: Return kielbasa to the pot. Stir in chicken broth, Better Than Bouillon, and bay leaves. Bring to a boil, then reduce heat and simmer uncovered for 20 minutes to develop flavor.
Add Chicken: Stir in cooked chicken and simmer another 5 minutes to heat through.
Cook the Tortellini: In a separate pot, boil tortellini in lightly salted water until just al dente (about 3–4 minutes). Drain well and set aside.
Finish the Soup: Stir spinach into the soup just until wilted. Remove bay leaves. Off heat, add lemon juice or vinegar to brighten. Taste and adjust seasoning.
Assemble + Serve: Ladle soup into bowls and add a spoonful of tortellini to each. Garnish with chopped parsley and Parmesan.