This hearty one-pot meal is the perfect dish for a crowd. Add a pan of cornbread and you've got a party!
In a large pot, heat 3 tbsp. oil over medium. Add the sausage. Cook, stirring often, until browned and crispy around the edges, about 10 minutes. Add half the onions. Cook, stirring often, until beginning to soften, 2 to 3 minutes. Add the remaining onions. Cook, stirring occasionally, until lightly browned, about 8 minutes. (Add the remaining 1 tbsp. oil if needed.) Add the beer. Stir, scraping up any browned bits from the bottom of the pot. Cook until the liquid is slightly reduced, about 2 minutes. Stir in the tomatoes, olives, and basil. Increase heat to medium-high. Bring to a gentle simmer.
Add a third of the cabbage to the pot. Cook, stirring often, until wilted, 4 to 5 minutes. Repeat 2 more times with the remaining cabbage. Reduce heat to medium-low. Cover and simmer, stirring occasionally, until the cabbage is tender, about 30 minutes. Season with salt and pepper. Add hot sauce to taste.