Preheat oven to 400°F (200°C).
Place chicken breasts on a flat surface and butterfly each by cutting horizontally through the center, being careful not to cut all the way through, to create a pocket.
Combine garlic powder, paprika, salt, and pepper in a small bowl; season the chicken breasts on all sides and inside the pocket.
Place one slice of provolone cheese and 3 to 4 asparagus spears into each chicken pocket.
Secure the edges of the chicken breasts with 2 to 3 toothpicks to keep the filling in place.
Heat olive oil and butter in a large oven-safe skillet over medium-high heat.
Sear the chicken for 3 to 5 minutes per side until a golden-brown crust forms.
Transfer the skillet to the oven and bake for 12 to 15 minutes, or until the internal temperature of the chicken reaches 165°F (74°C).
Remove from oven and let rest for 5 minutes; remove toothpicks before serving.