Heat one tablespoon of oil in your skillet over medium heat, then add the chopped onion and bell pepper. Cook for about five minutes, stirring now and then, until they soften and turn slightly golden at the edges. Stir in the minced garlic and cook for another minute until it smells fragrant. This base is what gives the beans their depth of flavor.
Add the pinto beans, reserved bean liquid, pico de gallo, smoked paprika, and cumin to the skillet. Pour in the cup of water and bring everything to a gentle simmer. Let it bubble away, stirring and mashing occasionally with a potato masher, so the beans break down into a thick, spreadable mixture.
Keep cooking the beans for about eight to ten minutes, until most of the liquid has absorbed and the texture looks creamy rather than soupy. If it looks too dry, splash in a bit more water. Taste and adjust with salt and pepper before pulling it off the heat.
Briefly warm each tortilla in a dry skillet or over a gas flame for a few seconds per side. This makes them soft and pliable, so they fold without cracking. Stack the warmed tortillas under a clean towel to keep them from drying out while you work.
Lay a tortilla flat and spread about a third of a cup of the bean mixture across the center. Sprinkle a generous handful of shredded cheese on top. Fold the two sides inward, then fold the bottom edge up and over the filling, rolling it tightly away from you into a snug burrito.
Heat the remaining oil in the skillet over medium heat. Place the burritos seam side down and cook for three to five minutes per side, turning occasionally, until every side is golden and crisp. This step gives you that irresistible crunchy shell with a molten center.
Let the burritos sit for a minute or two off the heat, since the cheese inside is extremely hot. Slice them in half on a diagonal to show off that gooey, melty middle, then serve right away with sour cream and hot sauce on the side.