Heat olive oil in a medium saucepan over medium-low heat. Add garlic and cook briefly until fragrant. Add tomatoes, chipotle peppers plus adobo sauce, oregano, and a pinch of salt. Bring to a simmer then reduce heat to low and gently simmer, stirring occasionally.
Meanwhile heat 2 tbsp canola oil in a large cast iron skillet over medium heat. Working in batches, fry tortillas for 1-2 minutes per side until browned and crisp. Remove to a wire rack.
Add 1 tbsp oil to the skillet then add chorizo and cook 5-6 minutes, stirring occasionally, until starting to brown. Add pinto beans and continue to cook, stirring occasionally and gently smashing beans with the back of spoon, for 2-3 minutes until beans are fairly smooth. Remove from heat.
Assemble pizzas: Spread ¼ cup of tomato sauce on top of two tortillas, covering completely. Divide chorizo-bean mixture onto remaining two tortillas and spread to cover. Place chorizo-bean tortillas on top of tomato covered tortillas, filling-side-down. Top with remaining tomato sauce and shredded mozzarella cheese.
Fry eggs in a nonstick pan: Melt butter over medium heat. Crack eggs into pan. Sprinkle with salt and pepper. Cook until white is completely set, about 2-3 minutes. Serve as is for sunny-side-up, or flip and cook to desired doneness.
Top pizzas with fried eggs. Top with cilantro and hot sauce.