Preheat oven to 375°F (190°C). Lightly grease an oven-safe skillet if needed.
Rub chicken breasts with olive oil and season generously with salt and pepper. Heat skillet over medium-high heat and sear chicken for about 5 minutes per side until golden brown.
Add minced garlic and cook for 30 seconds until fragrant. Pour in chicken broth, scraping the pan to release browned bits. Reduce heat and stir in sour cream until smooth.
Top each chicken breast with shredded Jack cheese. Transfer skillet to the oven and bake for 12–15 minutes, until cheese is melted and chicken reaches 165°F.
Remove from oven and garnish with chopped green onions and paprika. Serve hot.
