Heat oven to 350°.
Place cod on a baking sheet and season with salt and pepper; drizzle with oil.
Bake until cod is cooked through, about 15 minutes.
Melt butter in a small saucepan over medium; stir in eggs and cook until eggs are heated through, 1–2 minutes.
spoon sauce over the top of the cod filets
Garnish with parsley;
serve with lemon wedges.