Prepare a grill for medium heat. Wearing thin gloves, use a sharp paring knife, held at a 45-degree angle to the paddles, to carefully remove the spines. Make 3 to 5 slits in the skin of the cactus and rub all over with the garlic clove, then the oil. Sprinkle with some salt.
Lightly oil the grill grates. Grill the nopales cactus until lightly charred, and the pad becomes tender, flipping once, 10 to 15 minutes total. Set aside to cool, then cut into 1/4-inch strips.
For the ancho chile puree:
Place a dry, nonstick pan over medium heat and lightly toast the chile, turning occasionally,10 minutes. Turn the heat off and step back from the pan to add 3 tablespoons of water, being careful not to let the steam burn you. Cover and let the chile soak 15 minutes.
Transfer the chile with its water to a blender with a pinch of salt and puree until smooth, adding more water if needed. Combine 3 tablespoons of the resulting paste with the olive oil and the remaining 2 to 3 pinches of salt, or more to taste. (Save the rest of the paste for another use.).
For the roasted tomato salsa:
Combine the tomatoes, quartered Serranos and onions in a large bowl. Toss with the canola oil. Spread the tomatoes, onions, quartered Serranos, 1 clove garlic and bay leaf in a baking pan. Place under the broiler and char until nicely colored, stirring occasionally, 5 to 8 minutes.
Meanwhile, place the dried ancho chiles in a container of water and allow to hydrate, 20 minutes.
Sprinkle the broiled vegetables evenly with the paprika, then toss to coat and return to the broiler, about 1 minute. Watch carefully and do not allow the paprika to burn. Remove from the broiler. Stir in the chopped Serranos, ancho chiles (discard the water), chile flakes and olive oil. Allow to marinate in the pan at room temperature, tossing occasionally, 30 minutes. Remove and discard the bay leaf.
Chop the tomatoes and stir them together with the other vegetables in a bowl, tearing off and adding small amounts of toasted bread as needed to thicken. Add the vinegar and salt and pepper to taste.
Mince the remaining clove garlic. Stir into the salsa along with the cilantro, lime juice and Mexican oregano. Stir in additional salt to taste.
For the avocado crema:
Combine the avocado flesh, lime juice, orange juice, lemon juice, cilantro and salt to taste in a food processor, and pulse until pureed. Pass through a fine-mesh strainer and adjust seasoning to taste.
For the tacos:
Place the tortillas on a serving plate. Spread with the ancho chile puree using the back of a spoon. Arrange a thin layer of nopales cactus strips over the ancho chile puree. Add a layer of shredded lettuce and spoon some roasted tomato salsa over the top. Drizzle with some avocado crema, and sprinkle with the cheese. Serve immediately.