Heat 1 Tbsp olive oil in a medium saucepan over medium-high heat. Add ground turkey to the pan. Brown the meat, breaking it up into very small pieces as it cooks.
Remove meat from the pan, and season with salt and ground black pepper, if desired; reserve.
Return pan to the stove. Add remaining 2 Tbsp of olive oil to pan, and heat over medium heat. Add garlic, onion, and pepper, and cook until soft.
Add meat back to the pan, and stir in beans, tomatoes, and cumin. Heat to boiling, then simmer for 10 to 15 minutes.