Make the meatballs: Preheat the oven to 400 degrees F and brush a baking sheet with olive oil. Pulse the bread in a food processor to make coarse crumbs. Transfer to a small bowl, add the milk and set aside to soak. Lightly beat the eggs in a large bowl, then add the beef, parsley, parmesan, garlic, 1 teaspoon salt and the red pepper flakes; mix with your hands to combine. Add the bread-milk mixture and mix until just combined (do not overmix).
Dampen your hands and shape the meat mixture into 4 large balls. Make an indentation in the center of each with your thumb and stuff with a mini mozzarella ball, then mold the meat around the cheese. Arrange the meatballs on the prepared baking sheet and bake until browned and firm, 25 to 30 minutes.
Meanwhile, make the sauce: Heat the olive oil in a large deep skillet over medium-high heat. Add the garlic and red pepper flakes and cook, stirring, until the garlic softens, about 1 minute. Add the tomatoes, 1 cup water, the basil sprigs and 1/2 teaspoon salt. Bring to a boil, then reduce the heat to low and simmer until thickened, about 30 minutes.
Remove the meatballs from the oven and add to the sauce, spooning some of the sauce on top. Continue cooking, occasionally spooning the sauce over the meatballs, until tender and cooked through, about 6 minutes. Serve with ricotta and chopped basil.
You can form all of these meatballs a day ahead; cover and refrigerate until ready to cook.