Prepare the jalapeños. Put on gloves before handling the peppers. Slice off the tops, then hollow them out using a sharp paring knife or a special pepper coring tool, carefully removing all the seeds.
Make the filling. Mix the cream cheese and shredded cheddar in a mixing bowl using a fork until smooth and well-mixed.
Stuff the peppers. Use a spoon to fill the hollowed jalapeños with the cheese mixture, pressing it firmly to avoid air pockets.
Prepare the breading. In one bowl, whisk together the eggs and milk. Mix the flour, panko breadcrumbs, salt, and black pepper in another bowl.
Bread the peppers. Dip each stuffed pepper into the egg mixture, then into the flour mixture, making sure it’s well-coated. Repeat this process to form a thick, sturdy breading.
Fry the peppers. Heat the oil in your deep fryer, Dutch oven, or skillet to 375°F. Fry the breaded jalapeños in batches for 3-4 minutes, turning once until golden brown and crispy. Use tongs to transfer the fried peppers to a plate lined with paper towels to drain any excess oil.
Serve. Serve the jalapeño poppers immediately with ranch dressing, sour cream, or your favorite dipping sauce.