Heat oil in a 12-inch nonstick skillet over medium-high heat until shimmering. Add the poblanos, bell peppers, and salt, then cook while stirring occasionally until the peppers are softened and show light brown charred spots, about 10 to 12 minutes. Transfer the peppers to a bowl and cover to keep warm, then wipe out the skillet with paper towels.

Mix the masa harina and salt in a medium bowl, then stir in the water with a rubber spatula until combined. Knead the mixture in the bowl by hand until a soft, slightly sticky dough forms, 1 to 2 minutes; cover the bowl with a wet dish towel and let the dough rest for 5 minutes.

Adjust an oven rack to the middle position and heat the oven to 200°F. Place a wire rack inside a rimmed baking sheet and set it in the oven to keep the finished cakes warm. Divide the dough into six equal pieces and roll each into a 5-inch-long rope on a parchment-lined sheet, keeping them covered with the damp towel so the masa doesn't dry out.

Working with one piece of dough at a time, place the rope between two heavy plastic squares (cut from a zipper-lock bag) and press flat using a flat-bottomed pot or pie plate until it forms an oval 1/8-inch thick. Remove the plastic and return the shaped dough to the prepared sheet, keeping it covered while you shape the rest.

Heat some of the remaining oil in the skillet over medium-high heat until shimmering. Place two pieces of dough in the skillet and cook until dark brown spots appear on the first side, 4 to 6 minutes, then flip and continue to cook until the second side is crisp and set, 2 to 4 minutes. Transfer the huaraches to the wire rack in the oven and repeat with the remaining oil and dough in batches.

Spread a portion of the warm beans in an even layer over each huarache, leaving a small border around the edge. Distribute the pepper mixture evenly over the beans and sprinkle with queso fresco. Serve warm with the pickled shallots and radishes.