Heat a splash of olive oil in a large heavy-bottomed pot over medium heat until shimmering. Add diced onion and cook, stirring occasionally, until golden and fragrant, about 5 minutes.
Add minced garlic to the pot and cook for about 30 seconds until it releases a fragrant aroma.
Push the vegetables to the side of the pot and add ground turkey. Break it apart with your spoon and cook until browned and no longer pink, about 8 minutes. You should hear a gentle sizzle as it cooks.
Stir in chili powder, cumin, and smoked paprika, cooking for about 1 minute to toast the spices and deepen their aroma.
Pour in the crushed tomatoes along with a splash of vegetable broth. Stir well to combine everything, and bring the mixture to a gentle simmer.
Reduce the heat to low and let the chili simmer uncovered for 30 minutes, stirring occasionally. It should thicken slightly but remain saucy, and the flavors will deepen.
Taste the chili and add salt and pepper as needed to enhance the flavor.
Serve the chili hot, garnished with chopped cilantro and a squeeze of fresh lime for brightness and freshness.