Heat large skillet on high heat, on stove-top. Add olive oil. Add chicken thighs, generously seasoned with salt and pepper, to the skillet, skin side down. Cook until the skin turns golden and crispy - about 5 minutes, maybe less (depends on your stove). After the skin turns golden color and gets crispy, flip chicken over to the other side. Remove the skillet from heat. Let the chicken continue cooking like that, off heat.
Prepare the baking sheet. Remove chicken from the skillet onto the baking sheet, skin-side up. Add asparagus to the baking sheet. Sprinkle asparagus with about 2 tablespoons of oil from the skillet where you just cooked the chicken thighs. Sprinkle salt and pepper over asparagus.
Bake the chicken and the asparagus in the oven preheated to 400 F for 25 minutes or until the chicken is completely cooked through and the juices run clear.
While the chicken is baking, clean the skillet with the paper towel. Add 1 tablespoon olive oil, sun-dried tomatoes (drained from oil), minced garlic. Cook for about 1 minute, constantly stirring.
Add half and half and paprika. Bring to boil. Add cheese and stir until the cheese starts melting. Reduce heat to medium and continue stirring until the sauce is creamy. Remove from heat.
Once the chicken is cooked, add the cooked chicken and the cooked asparagus to the same skillet. Reheat the sauce if needed. Sprinkle with freshly chopped parsley. Serve.