Add the garlic and cook until crisp and golden brown, about 5 minutes. Careful not to burn. Burnt garlic tastes bitter. Use a slotted spoon to transfer the garlic to a paper towel-lined plate. Set aside. Add the butter to the skillet and set over medium-high. When the butter has melted, add half of the asparagus with the tips pointing in one direction, and the remaining spears pointing in the opposite direction. (This improves browning.) Sprinkle the asparagus with 1/4 teaspoons salt; using tongs, arrange the spears in an even layer. (They won't quite fit into a single layer.) Cover and cook until the spears are bright green and still crisp, about 5 minutes.
Season with salt and pepper, then transfer the asparagus to a serving plate. Sprinkle with the toasted garlic and Parmesan cheese. Serve with lemon wedges.