Put the meat in a large bowl and mix together with your hands. Add a good pinch of kosher salt, the chile flakes, fennel seeds, cayenne, breadcrumbs, and Parmesan. Mix to blend and then form the meat into small 2-inch patties.
Heat the canola oil in a large skillet over high heat. When the oil begins to smoke lightly, shut off the heat to avoid splattering, and add the meat patties in a single layer in the pan. Take care they are spread somewhat apart so they have a chance to brown instead of steam. Put the heat back on high and brown them, turning them so they brown all around, 3 to 5 minutes on each side. Touch them to make sure they are still tender and somewhat yielding in the center. Use a slotted spoon or spatula to remove them from the pan. Transfer the patties to a platter or individual plates.
Use a kitchen towel to wipe clean the skillet, put the heat on medium, and add the butter. When it begins to brown, crack 2 eggs, a distance apart, into the butter. Lower the heat, season the eggs lightly with salt, and cook 2 to 3 minutes or longer, if desired. Repeat with additional eggs. Put the eggs on the patties and serve immediately.