Prepare the gnocchi according to the package directions; drain and set aside.
Heat 2 teaspoons olive oil in a large skillet over medium-high heat; add the minced shallots and garlic and sauté 2–3 minutes until soft and fragrant.
Transfer the cooked shallots and garlic to a food processor or blender. Add the drained roasted red peppers and 1/2 cup broth and blend until smooth.
Pour the pepper puree back into the skillet and bring to a simmer over medium heat. Stir in the half and half, 1/4 cup Pecorino Romano, 1/2 teaspoon kosher salt, and fresh black pepper to taste; heat until warmed through.
Add the baby spinach to the sauce and cook 4–5 minutes, stirring, until wilted.
Add the cooked gnocchi and sliced grilled chicken to the skillet and toss gently to coat in the sauce and warm the chicken through.
Stir in the chopped fresh basil, then serve in bowls with extra Pecorino Romano if desired.
Notes
Use either chicken or vegetable broth based on preference.
Drain roasted peppers well to avoid thinning the sauce.
Slice the grilled chicken thinly for easy tossing.
Whole-grain or alternative gnocchi may be substituted if desired.