Prepare breading stations:

Arrange two pie plates or shallow baking dishes. In the first, beat eggs with 1 1/2 cups milk until combined. In the second, stir together 2 cups flour, cayenne, salt, and black pepper.

Season pork chops:

Sprinkle both sides of the pork with salt and pepper.

Double coat pork chops:

Coat each pork piece first in the egg mixture, then the flour mixture, then back in the egg mixture, and finally in the flour mixture again. Place on a plate.

Heat oil in skillet:

Pour about 1/4 inch of canola oil into a large skillet and heat over medium-high until shimmering.

Fry pork chops:

Fry each pork chop for 2-3 minutes per side, until golden and fully cooked (internal temperature reaches 145°F (65°C)/63°C). Transfer to a paper towel-lined plate to drain.

Make roux for gravy:

In a medium saucepan over medium heat, melt butter. Whisk in 1/4 cup flour, salt, pepper, and 1/8 tsp cayenne. Cook, whisking constantly, for 3-5 minutes until bubbly and light golden.

Add milk and thicken:

Gradually pour in 2 cups milk while whisking continuously to avoid lumps. Continue cooking, whisking occasionally, until the gravy thickens, about 10-12 minutes. Season to taste.

Serve with gravy:

Pour the gravy over the pork chops and serve.