Pour oil into a 10- to 12-inch ovenproof frying pan over high heat; when hot, add onions and stir often until slightly limp and beginning to brown, about 4 minutes.
Stir in beer and thyme; cook until liquid is reduced by about half, 3 to 5 minutes.
Stir in salt and pepper to taste.
Pick sausages all over with the tip of a sharp knife and arrange in a single layer on onions mixture.
Bake in a 375°F regular or convection oven until sausages are heated through, about 20 minutes. Sprinkle with parsley.