Soak dried chiles in boiling water for 15 minutes to soften.

Drain chiles, reserving the soaking liquid. Remove stems and seeds.

Blend chiles, tomatoes, onion, garlic, jalapeno, paprika, and 1 cup of reserved soaking liquid until smooth.

Heat vegetable oil in a saucepan over medium-high heat.

Add the chili puree to the saucepan and bring to a boil, then reduce heat and simmer for 15 minutes, stirring occasionally, until slightly thickened.

Stir in honey and season the sauce to taste with salt and pepper.

Heat vegetable oil in a skillet to 350°F for frying.

Fry tortilla quarters in batches until crisp, about 2-3 minutes per batch.

Transfer fried tortillas to a wire rack on a baking sheet and season with salt.

Preheat broiler.

Toss fried tortilla chips with 1 cup of the sauce in a bowl.

Transfer half of the chips to an ovenproof platter or skillet.

Scatter half of the queso fresco and Monterey Jack cheeses over the chips.

Top with the remaining chips, cheeses, and 1/2 cup more sauce.

Broil until the cheese is melted and golden, about 4-5 minutes.

Meanwhile, heat oil in a nonstick skillet over medium heat.

Fry eggs until the whites are set and the yolks are still runny, about 4 minutes.

Top the chilaquiles with chopped onion, radishes, cilantro, and lime wedges.

Top with fried eggs and serve with the remaining sauce alongside.