Pat the chicken dry and season both sides with salt and black pepper. If breasts are thick, halve them horizontally or pound to an even 1/2-inch thickness so they cook evenly.
Heat 1 tablespoon olive oil in a large oven-safe skillet over medium-high heat. When the oil shimmers, add the chicken and sear undisturbed until golden, about 3–4 minutes per side. Transfer the chicken to a plate (it will finish cooking later).
Reduce the heat to medium. Add 1 tablespoon olive oil to the same skillet if needed, then sauté the minced garlic and chopped sun-dried tomatoes for about 1 minute until fragrant, scraping up any brown bits from the bottom of the pan.
Pour in the chicken broth and bring to a gentle simmer, scraping the pan. Let the liquid reduce for 2–3 minutes so it concentrates slightly.
Transfer the hot tomato-broth mixture to a blender. Add the cottage cheese, grated Parmesan, lemon zest and red pepper flakes. Blend until completely smooth and creamy (this is the key to a silky, lower-fat sauce). Taste and adjust seasoning with a pinch of salt and pepper.
Return the blended sauce to the skillet and warm over low heat until it just begins to thicken, about 2 minutes. Stir in half the chopped basil.
Nestle the seared chicken back into the sauce. Spoon some sauce over each piece. Transfer the skillet to a preheated 375°F oven and bake until the chicken reaches 160–165°F and sauce is bubbling, about 8–10 minutes.
Remove the skillet from the oven and let the chicken rest in the sauce 5 minutes (it will continue to cook to the perfect temperature). Finish with the remaining basil and a little extra Parmesan if desired, then serve warm.