Heat the olive oil in a 12-inch skillet over medium heat. Add the diced onion and bell pepper and cook for 5 minutes, stirring occasionally, until the onion turns translucent.

Add the minced garlic and cook for 30 seconds until fragrant.

Push the vegetables to one side, add the ground turkey, and break it up with a wooden spoon. Cook for 6 to 8 minutes, stirring often, until no pink remains and the turkey reaches 165 F / 74 C on an instant-read thermometer.

Drain and rinse the cooked lentils, then stir them into the skillet along with the tomato sauce, ketchup, tomato paste, and Worcestershire sauce.

Add the brown sugar, smoked paprika, chili powder, salt, black pepper, and water. Stir to combine.

Bring the mixture to a gentle simmer, then reduce the heat to medium-low. Simmer uncovered for 10 to 12 minutes, stirring every few minutes, until the filling thickens enough to mound on a spoon instead of running off it.

Taste and add more salt if needed. If the mixture still looks loose after 12 minutes, keep simmering in 2-minute increments, it should look like a thick chili, not a soup.

Toast the buns cut-side down in a dry skillet or under the broiler for 1 to 2 minutes until lightly golden.

Spoon about 1 cup of the turkey and lentil filling onto each bun. Top with shredded cheddar and pickle slices if using, and serve right away.