Heat 1 Tablespoon olive oil in a large skillet over medium-high heat.
Season the 1 boneless skinless chicken breast pieces with salt and freshly ground black pepper. Add the chicken in a single layer and cook until golden on the bottom, about 2–3 minutes. Flip and cook an additional 2–3 minutes, until cooked through. Transfer the chicken to a plate.
Reduce heat to medium and add 1 1/2 Tablespoons butter to the skillet. Melt the butter, scraping up any browned bits from the pan.
Add 3 teaspoons minced garlic and sauté about 20 seconds, until fragrant.
Pour in 1 1/2 cups low-sodium chicken broth and 1/4 cup water, stirring to combine and to loosen any browned bits.
Add 10 ounces refrigerated cheese tortellini to the skillet. Increase heat to bring the liquid to a gentle boil, then reduce to a simmer. Cover and cook, stirring occasionally, until the tortellini are tender, about 3–5 minutes. Do not overcook.
Uncover and add 4 ounces Neufchatel cheese (in small pieces), 1/2 cup freshly grated Parmesan cheese, and 1 Tablespoon fresh lemon juice. Stir until the cheeses melt and form a creamy sauce.
Return the cooked chicken to the skillet and add 2 cups baby spinach leaves. Toss or stir until the spinach wilts and the chicken is heated through, about 1–2 minutes.
Taste and season with additional salt and freshly ground black pepper if needed.
Remove the skillet from heat, cover, and let rest for 2–3 minutes to allow the sauce to thicken slightly and the spinach to finish wilting.
Serve warm.