Line a baking sheet with parchment and place a wire rack over a second baking sheet for draining. Wear kitchen gloves. Halve the jalapeño peppers lengthwise, leaving stems on if attached. Use a small spoon to remove seeds and membranes.
In a bowl, mix cream cheese, sharp cheddar cheese, scallions, garlic powder, kosher salt, and black pepper until smooth and evenly combined.
Fill each jalapeño half with the cheese mixture, mounding slightly but keeping the top level for breading. Arrange filled halves on the parchment-lined sheet.
Set up a breading station: place all-purpose flour in one shallow dish. In a second dish, whisk eggs with milk. Put panko breadcrumbs in a third dish.
Dredge each filled jalapeño first in flour (tap off excess), then dip in the egg mixture, then coat thoroughly in panko breadcrumbs. Return to the sheet. For the best adhesion, refrigerate the breaded poppers for 20 minutes.
Pour vegetable oil into a deep, heavy pot to a depth of 2–3 inches and heat to 350°F (175°C). Maintain temperature between 340–360°F.
Fry the poppers in batches without crowding, 3–4 minutes per batch, turning once, until the crumbs are deep golden and the cheese just begins to melt. Doneness cue: exterior crisp and golden; pepper tender but still slightly firm. Transfer to the wire rack to drain.
Let poppers cool 5 minutes so the filling sets slightly. Serve warm with ranch dressing for serving.