Heat the oven to 450 and line a baking sheet with parchment. Spread the eggplant pieces on the try and toss with 1/4 cup of the oil and 1/2 tsp salt and some pepper. Spread them out as much as possible. Bake for 30 minutes and then cool slightly.
Chop the eggplant until it is a chunky mash. Add the ricotta, parmesan, egg, yolk, flour, breadcrumbs, half the garlic, 1/2 the basil, 1/4 tsp salt, and some pepper. Mix well with your hands. If the mixture is too wet add some extra bread crumbs or flour. You should be able to form balls that hold together, but they should not be dry.
Heat 2 tbsp of oil in a skillet and form golf ball sized balls of the mixture. Cook half of them, browning on all sides and set aside. Add 2 more tbsp of oil and fry the other half.
Reduce the oven to 400. To make the sauce, place a little oil into a sauce pan and add the rest of the garlic. Sautee a bit then add the crushed tomatoes, tomato pasted, sugar, chile flakes, paprika, oregano and 1 tsp of salt. Simmer for a few minutes then add the cup of water and continue to simmer about 10-15 minutes until thickened.
Pour the sauce into a 9x13 inch pan and nestle the dumplings into the sauce. Bake for 20 minutes until hot and bubbling and then top with the rest of the basil and grated parm and serve. I served over pappardelle.