In a large stockpot, warm the olive oil. Cook the onion over medium heat with a pinch of salt, stirring often, until softened, about 8-10 minutes. Stir in the spice paste and cook 1 minute, stirring the whole time so it doesn’t burn. Add the turkey and salt and stir vigorously with a spoon, breaking up the meat. Add the tomatoes, cook another 4-5 minutes, scraping up any bits from the bottom of the pot. Stir in the broth and beer if using, and the squash or pumpkin, then partially cover and cook 45 minutes until thickened.