For the eggplant: Line 1 baking sheet with several layers of paper towels and another baking sheet with parchment paper. Use a little grapeseed oil to lightly grease 3 (9- by 13-inch) baking dishes (or several smaller shallow baking dishes). Place the flour in a medium bowl; whisk the eggs and cheese together in a separate mixing bowl, then whisk in the parsley, oregano, salt, black pepper and crushed red pepper flakes; place half the breadcrumbs in a third (medium) bowl.
Coat each eggplant slice in the flour, then in the egg-cheese batter, then in the breadcrumbs, making sure each slice is completely coated. Place them on the parchment-paper-lined baking sheet as you work. Add more of the remaining breadcrumbs as needed.
For the sauce: Heat the olive oil in a deep, heavy-bottomed 5-quart pot over medium-low heat. Stir in the garlic; cook, but do not brown, until the oil is well scented. Remove and discard the garlic; increase the heat to medium and add the anchovies and butter, letting the butter foam and sizzle. Use a wooden spoon to break up the anchovies.
Stir in the onions; cook, stirring occasionally, for 10 to 14 minutes or just until translucent. Stir in the tomatoes; once they start to bubble at the edges, cook uncovered for 40 minutes, stirring occasionally, until thickened and saucy. Stir in the basil, salt and pepper; turn off the heat. Taste, and add salt and/or pepper as needed.
Heat 3 tablespoons of the grapeseed oil in a large, wide skillet over medium heat. Once the oil shimmers, add enough eggplant slices to fit in a single layer. Fry for 3 or 4 minutes per side, until well browned and crisped. Transfer to the paper-towel-lined baking sheet as you work. Repeat to use all the eggplant, changing the oil (another 3 tablespoons heated each time) and wiping out the skillet every two or three batches, or the burnt bits will accumulate and turn the oil black and bitter.