Heat oil in a 12-inch nonstick skillet over medium-high heat until shimmering. Add the poblanos, bell peppers, and salt and cook, stirring occasionally, until the peppers are softened and lightly browned, 10 to 12 minutes. Transfer the peppers to a bowl and cover to keep warm; wipe the skillet clean with paper towels.

Mix the masa harina and salt in a medium bowl, then stir in the water with a rubber spatula. Use your hands to knead the mixture in the bowl for 1 to 2 minutes until a soft, sticky dough forms. Cover the dough with a wet dish towel and let it rest for 5 minutes.

Adjust the oven rack to the middle position and heat the oven to 200°F. Set a wire rack inside a rimmed baking sheet and place it in the oven to keep finished cakes warm. Line a second baking sheet with parchment paper. Cut a quart-size plastic bag into two equal squares to use as a pressing surface.

Divide the dough into 6 equal pieces and roll each into a 5-inch-long rope. Working with one piece at a time, press the dough rope between the plastic squares using a flat-bottomed pot or pie plate until it forms a 1/8-inch-thick oval. Keep the shaped and unshaped dough covered with a wet towel at all times to prevent drying.

Heat 2 teaspoons of oil in the empty skillet over medium-high heat and swirl to coat. Place two pieces of dough in the skillet and cook until dark spotty brown on the first side, 4 to 6 minutes. Flip and cook until the second side is crisp, 2 to 4 minutes. Transfer to the wire rack in the oven and repeat with the remaining oil and dough in two more batches.

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