Heat the oven to 375°F. Lightly grease a 12-cup muffin tin or line 8 cups with paper liners.
Warm the olive oil in a large skillet over medium heat. Add the mushrooms and onion, and cook for 8 to 10 minutes, stirring often, until the mushrooms have released their moisture and the pan is mostly dry. Stir in the garlic and cook for 30 seconds. Let the mixture cool slightly.
Add the lentils to a mixing bowl and mash them with a fork until about half are broken down. Stir in the cooked mushroom mixture, egg, breadcrumbs, 2 tablespoons of the barbecue sauce, tomato paste, smoked paprika, thyme, salt, and black pepper. Mix until evenly combined.
Divide the mixture among 8 muffin cups, pressing it down lightly. Spoon the remaining barbecue sauce over the tops.
Bake for 25 to 30 minutes, until the muffins are set and the glaze looks sticky. Let them rest in the tin for 5 minutes before removing so they hold their shape.