Pour boiling water over chiles in a heatproof bowl. Submerge chiles under the water with a second, smaller bowl and let soak until soft, about 30 minutes.
Pour chiles and water into a blender and blend until smooth. Strain, reserving liquid.
Place chile water in a medium saucepan and add ¼ cup oil and salt. Bring to a boil over medium heat. Add flour and beat with a wooden spoon until a smooth dough forms and starts to peel away from the sides of the pan.
Transfer dough to the bowl of a stand mixer fitted with the paddle attachment. Start mixing on low, add the egg, and then increase speed to medium. Beat for 2 minutes. Add panela cheese and beat just until incorporated.
Place a star-shaped tip in a heavy-duty piping bag (a small tip works best as they cook faster). Fill piping bag up ¾ of the way with dough, and twist the end until it pushes the dough into the tip.
Fill a deep pot with 2 quarts of oil and attach a deep-fat fry thermometer to the side if you have one. Heat the oil over medium-high heat until it reaches 350°F.
Meanwhile, pipe churros onto a parchment-lined baking sheet, cutting with scissors into 6-inch long tubes. Place churros in the refrigerator while you wait for the oil to heat.
Once oil is ready, carefully place churros in hot oil, 4-5 at a time, moving them around a little so they don’t stick to the bottom. Let fry, turning once until crisp and cooked through, about 4 minutes. Transfer to a paper towel-lined baking sheet. Repeat with remaining churros.
To serve: Place on a serving tray and sprinkle with Cotija, cilantro, and sea salt.
Cook’s Note or helpful tip (optional): Churros can be piped, covered and kept in the refrigerator up to a day in advance.