Preheat oven to 400°. Using a sharp knife, make a horizontal cut into thick side of each chicken breast, cutting almost to the end. (Be careful not to cut all the way through.)
Stuff each piece of chicken with mozzarella, tomatoes, and asparagus; season with a pinch of salt and pepper inside. Press edges of chicken together and secure with a toothpick.
In a small bowl, mix oregano, thyme, paprika, garlic powder, onion powder, 1 1/4 teaspoons salt, and 1/4 teaspoon pepper. Season outside of chicken all over with spice mixture.
In a large ovenproof skillet (preferably cast-iron) over medium-high heat, heat oil. Cook chicken, turning halfway through, until golden brown, about 4 minutes per side.
Transfer skillet to oven and bake until chicken is cooked through and an instant-read thermometer inserted into thickest part registers 74°C, 8 to 10 minutes.
Add butter and lemon juice. Swirl until butter melts, about 30 seconds. Remove toothpicks from chicken.
Divide chicken among plates. Spoon pan sauce over.
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