Add oxtails, enough water to cover the ox tails + 2 inches, garlic cloves, and seasonings into Dutch Oven or large pot over medium high heat and bring to a boil. Once it is consistently boiling turn down to low/medium and put the lid on. Cook until tender, about 2 hours.
Cut corn cobs into 3rd or 4ths and add into pot with halved baby potatoes with sausage slices if you want to add more meat such as this. Keep on low heat, covered for 1 more hours.
When everything is tender to your liking, drain liquid and serve oxtail boil pieces with a little bowl of melted butter and/or a squeeze of fresh lemon on top.