Heat the oil in a heavy-bottom 8-quart stockpot over medium-high heat. Add the onions and cook until slightly browned, 8 to 10 minutes.
In layers, add the salt, pepper, potatoes, corn, sausage, clams, mussels and shrimp. Add the beer and thyme. Cover and bring to a boil, about 10 minutes. Lower the heat and simmer until the potatoes are tender and the clams and mussels are all open, about 20 minutes more.
Transfer to a large platter, sprinkle with the parsley and serve.