Heat 1 tablespoon olive oil in an extra-large skillet or large pot over medium-high heat.
Add the minced garlic and sauté about 30 seconds, until fragrant.
Add the turkey sausage, break it up with a spoon, and cook, stirring occasionally, until no longer pink and cooked through.
Stir in the marinara sauce, diced tomatoes, chicken broth, and 1/2 cup water, then bring the mixture to a light boil.
Add the refrigerated tortellini, gently press the tortellini into the sauce so they are submerged, then reduce heat to medium-low, cover, and simmer until tortellini are cooked through, about 10 minutes, stirring once halfway through.
Stir in the chopped spinach and parsley, season with freshly ground black pepper (and salt only if needed), and toss gently until the spinach wilts.
Stir in the chopped basil, adjust seasoning if necessary, and serve warm.