1. In a 10- to 12-inch ovenproof frying pan over high heat, frequently stir onions in oil until somewhat limp and beginning to brown, about 4 minutes. Stir in stout and thyme; cook until liquid is reduced by about half, 3 to 5 minutes. Stir in salt and pepper to taste.
2. Prick sausages all over with the tip of a sharp knife and arrange in a single layer on onion mixture.
3. Bake in a 375° regular or convection oven until sausages are heated through (cut to test), about 20 minutes. Sprinkle with parsley.