In medium pot over medium heat, warm the olive oil until shimmering. Add the diced onion, pepper, carrot, and ½ teaspoon of the salt. Stir to combine and cook, stirring occasionally, until the vegetables are tender and the onion is translucent, about 3 minutes.
Add the garlic, chili powder, cumin, smoked paprika and oregano. Cook and stir constantly until the spices coat the veggies and become fragrant, about 1 minute.
Add the crushed tomatoes, drained beans, tomato paste, water and bay leaf. Stir to combine and let the mixture come to a simmer. Continue cooking, stirring occasionally while the chili simmers, about 30 minutes. Add 1 tsp of salt, stir and taste. Add additional seasonings as needed.
Remove the chili from the heat and discard the bay leaf.
Add the lime juice and garnish with your choice of toppings.
Serve with tortilla chips.