In a large pot, heat 3 tablespoons olive oil over medium-high heat. Add the turkey and cook, breaking it up, until browned, 7 to 10 minutes. Season with salt and pepper; using a slotted spoon, transfer the turkey to a plate.
Add the remaining 2 tablespoons olive oil to the pot and stir in the onion and jalapeno; cook until softened, about 5 minutes. Stir in the chili powder, cumin and oregano and cook for 1 minute more. Stir in the tomatoes and their juice, the beer and 2 cups water, scraping up any browned bits from the bottom of the pan. Stir in the rice and 1/2 teaspoon salt. Bring to a boil, then lower the heat, cover and simmer for 35 minutes. Stir in the turkey, cover and cook until the rice is tender, 20 to 25 minutes. Season with salt and pepper. Serve with the toppings.