Preheat the oven to 450°. Invert a 6-cup muffin tin and spray the underside with vegetable oil cooking spray.
Stir together the biscuit mix, milk and cayenne in a medium mixing bowl. Shape into a ball. Turn out onto floured surface and knead 2 to 4 times. Divide the ball into 6 pieces. Roll each piece into a 6-inch circle. Place 1 dough circle over each muffin cup. Press around the cup to form a bowl shape. Bake for 12 to 15 minutes, until lightly browned. Let cool slightly. Remove the biscuit bowls and reserve.
Brown the ground chuck over medium heat in a Dutch oven. Add the onions and green pepper and continue to cook until the meat is completely browned and the vegetables are tender. Add garlic and cook until fragrant. Drain of any fat and discard. Stir in the tomatoes, beans, chili powder and salt. Bring the mixture to a boil, cover, and reduce the heat to low. Simmer for 35 minutes. Season with ground black pepper. When ready to serve, spoon hot chili into the biscuit bowls. Garnish with shredded Cheddar, sour cream, sliced green onions, and corn chips.