Pat steak cubes completely dry with paper towels. Toss in a mixing bowl with 1 tbsp olive oil, 1 tsp kosher salt, 1/2 tsp black pepper, and paprika until coated. Let rest at room temperature for 10 minutes.
Heat 1 tbsp olive oil and 1 tbsp butter in a large heavy cast-iron skillet over high heat until shimmering and nearly smoking.
Add steak bites in a single layer without crowding the pan. Sear undisturbed for 2 minutes to form a deep caramelized crust. Flip and cook for another 2 minutes until browned on all sides.
Add 2 tbsp butter, half of the minced garlic, and minced rosemary to the skillet. Baste the foaming herb butter vigorously over the steak bites for 1 minute. Transfer steak bites to a warm plate and tent loosely with foil.
In the same skillet over medium heat, melt remaining 1 tbsp butter in the flavorful pan drippings. Add trimmed asparagus spears and cook for 3 to 4 minutes, rolling occasionally, until tender-crisp with blistered edges.
Stir in remaining minced garlic, 1/2 tsp salt, and remaining pepper during the last minute of cooking. Remove from heat and toss with a squeeze of fresh lemon juice.
Plate tender asparagus beside the seared steak bites, dusting asparagus generously with freshly grated Parmesan cheese. Spoon golden garlic pan drippings over the steak bites, garnish with chopped parsley, and serve immediately with fresh lemon wedges.