Pat pork chops dry, season with salt, pepper, and paprika; trim asparagus, toss with 1 tablespoon butter on a sheet pan, roast at 425°F for 10 minutes alongside pork cooking.
Heat a large skillet over medium-high, add 1 tablespoon butter, sear pork chops 5–6 minutes per side until golden and reaching 145°F internal temperature, remove to plates and rest 2 minutes.
In same skillet, add remaining 1 tablespoon butter and minced garlic, crack 4 eggs into skillet, fry 3–4 minutes until whites set and yolks still runny (or cooked to preference).
Top each pork chop with one fried egg, serve with roasted asparagus on the side.