Season salmon generously with salt and pepper and allow to come to room temperature for at least 10 minutes.
Warm olive oil in a 10-inch skillet (preferably cast iron) over medium heat. Swirl skillet to coat in oil.
Sear salmon flesh-side down for 3 minutes, until golden brown and crisp. Flip salmon. Add 1 tablespoon butter to the skillet and use a spoon to baste the salmon with the melted butter for an additional 3 minutes. Transfer salmon to a holding plate.
Add remaining butter, shallot, and garlic to skillet and cook for 2 to 3 minutes, until shallot and garlic are softened. Add asparagus and cook for 4 minutes, until not quite crisp-tender (take a bite!). Add fresh or frozen peas and cook until bright green and tender, but not mushy, about 2 minutes. Stir in parsley and juice of 1 lemon. Season to taste with salt and pepper.
Nestle salmon into the vegetables, skin-side down, for a few minutes to re-warm. Serve with lemon wedges.
