Preheat oven to 425°F. Heat garlic and 1 Tbs. oil in a small saucepan over medium-low. Cook, flipping garlic occasionally, until garlic cloves are blistered and lightly browned on all sides, 3 to 4 minutes. Remove from heat. Using a slotted spoon, remove and discard garlic cloves. Let oil cool in pan 2 minutes.
Add beans and salt to pan. Mash beans until a coarse paste forms; set aside.
Wrap tortillas in a damp paper towel, and place in medium microwave-safe bowl. Microwave on high until very hot and pliable, about 1 minute. Cover bowl with a plate or a lid, and let steam 2 minutes. Keep tortillas tightly covered while assembling taquitos. Pour remaining 2 Tbs. oil into a small bowl. Working with 1 tortilla at a time, lightly brush one side with oil. Flip tortilla, and spread 2 Tbs. bean paste on one end. Top bean paste with 1 Tbs. cheese. Starting at filling end, roll tortilla into a cylinder. Place seam side down on a parchment-lined baking sheet. Continue to repeat process, spacing the 8 taquitos evenly apart on baking sheet.
Bake in preheated oven until bottom sides of taquitos are lightly browned and crisp, about 12 minutes. Remove from oven. Flip taquitos, and return to oven. Bake until bottom sides are crisp, 6 to 8 minutes. Top with lettuce, tomato, sour cream, and avocado slices, if using.