Put on your food prep gloves. Slice each jalapeno open lengthwise using a paring knife, then make a small crosswise cut at the stem end to form a T.
Insert your (gloved!) fingertip through the top of the opening and gently wiggle the core loose, then remove. Rinse under cold water to remove any additional seeds. Pat dry gently with a paper or clean towel and set aside. Repeat with the remaining peppers.
Combine the Cheddar, Asiago, cream cheese and smoked hot sauce in a large bowl until smooth and well blended.
Gently nudge the cheese filling into each pepper with a spoon. To close the peppers, gently squeeze each one until it resembles its original shape. Don't worry if the peppers tear a bit, just squeeze them shut.
Sift together the breadcrumbs, paprika, 1 teaspoon salt and 1/2 teaspoon pepper in a shallow bowl.
Lightly beat the eggs in a second shallow bowl.
One at a time, hold the peppers by the stems and dip them in the beaten eggs, letting the excess drip off, and roll in the breadcrumbs; dip in the eggs again and reroll in breadcrumbs. Set on a plate to dry slightly.
In the meantime, heat 2 1/2 inches of the oil in a Dutch oven or heavy-bottomed cast-iron skillet until a deep-fry thermometer registers 325 degrees F. Add three or four of the jalapeno poppers, making sure not to crowd your pan, and fry in batches until golden and crisp, about 5 minutes. Keep an eye on the temperature of the oil and adjust the heat as necessary so it stays steady.
Remove with a slotted spoon and drain on a paper towel-lined plate; season with salt. Repeat with the remaining poppers and serve immediately.
Use regular breadcrumbs for this recipe, not panko.
Leftovers can be frozen flat and then stored in a freezer bag. Reheat in a 400 degrees F oven for 5 minutes.