Set your oven to 375°F (190°C) to preheat. Rub olive oil over the chicken breasts and season them well with salt and pepper.
Heat a skillet over medium-high heat and brown the chicken breasts on each side for about 5 minutes until nicely golden.
Add the minced garlic to the pan and sauté for around 30 seconds until it becomes aromatic.
Pour in the chicken broth and allow it to simmer, scraping the pan to lift any browned bits.
Mix in the sour cream thoroughly and let the sauce bubble gently for about 5 minutes to thicken.
Place the chicken breasts in a baking dish, spoon the creamy sauce over them, then sprinkle shredded Jack cheese on top.
Bake in the preheated oven for about 15 minutes or until the cheese is melted and bubbly.
Garnish the finished chicken with chopped green onions and a light dusting of paprika before serving.