These little guys are somewhat like gnocchi, but without the potato flour and (failed) attempts at piping them out of a bag. In Italian, gnudi means "naked", so you can think of them like the filling of a ravioli, but without the pasta wrapper. They're light and pillowy in a way that pasta or ravioli isn't. Basically, they're a delight. Plus, they're decidedly fancy for not a lot of work. I may even go so for as to say they're healthier than regular pasta or gnocchi because the shape is formed by strained ricotta instead of a boat-load of flour.
(Ok, not that healthy because they contain whole-milk ricotta (don't get the diet stuff. ick), but as far as health rankings go, I feel like current zeitgeist says carbs are the worst. So there's that.)
Make the breadcrumbs: Heat olive oil on medium heat in a small pan and toss in garlic. Once the garlic is fragrant, add in the bread, torn into chunks. Toss around on medium heat until the bread is toasted and crunchy, and the oil is absorbed, about 5-7 minutes. Transfer to a food processor and pulse until crushed (still chunky and not too fine).
Mix ricotta, egg, egg yolk, 1/2 parmesan, and 1/2 teaspoon salt in a large bowl until well combined. Add the breadcrumbs; stir until just combined and mixture forms a ball (mixture will be soft and moist with some bits of ricotta remaining; add more breadcrumbs by the tablespoon if it feels wet).
Dust a rimmed baking sheet generously with flour. Using 2 large soup spoons, shape heaping tablespoonfuls of dough into football shapes; place on a baking sheet and dust with more flour. Makes about 30.
Cook gnudi in a large pot of boiling salted water, stirring occasionally, until cooked through and tender, about 5-6 minutes. Gnudi will quickly float to surface; continue cooking or gnudi will be gummy in the center.
Using a slotted spoon, divide gnudi among bowls. Top with pomodoro sauce, more Parmesan and basil.