In a large bowl, add the breadcrumbs and the milk and stir until well-combined.
Let the breadcrumb mixture stand for 5 minutes.
Add the ground beef, the ground pork, the eggs, 2 of the chopped garlic cloves, 1 teaspoon of the salt, 1/2 teaspoon of the black pepper, 1 1/2 teaspoons of the sweet paprika, and 1/4 cup of the parsley to the breadcrumb mixture and knead the mixture gently until thoroughly combined.
Roll the meat mixture into 1 1/4-inch meatballs and transfer the meatballs to a baking sheet.
Cover the baking sheet with plastic wrap and refrigerate the meatballs until ready to cook.
In a saucepan or a Dutch oven over medium-high heat, add 3 tablespoons of the olive oil.
Add the onions, the carrots, and the remaining chopped garlic cloves to the saucepan and cook, while stirring, until the onions start to caramelize, about 15 minutes.
In a bowl, add the whole tomatoes and using a fork, mash them into a purée.
Add the tomato purée, the remaining sweet paprika, the extra salt, and the extra pepper to the pot and cook, stirring occasionally, until the liquid starts to evaporate, about 10 minutes.
Add the wine and the chicken stock and stir to combine.
Bring the tomato mixture to a boil.
Reduce the heat to medium-low.
Simmer the tomato mixture, while stirring occasionally, until it thickens slightly and the flavors meld together, about 20-30 minutes.
Taste the tomato mixture and add the extra salt and the extra pepper, as needed.
While the tomato mixture is simmering, in a large, nonstick skillet over medium-high heat, add the remaining olive oil.
Unwrap the meatballs and gently roll them in the flour, shaking off any excess.
Add the flour-coated meatballs to the hot oil and cook them on all sides until browned, about 5-8 minutes. Repeat until all of the meatballs are browned.
Transfer the meatballs to a plate to rest at room temperature until the tomato mixture is ready.
Once the tomato mixture is ready, add the meatballs and gently stir to combine and thoroughly coat the meatballs.
Simmer until the meatballs are cooked through, reaching an internal temperature of at least 155 degrees F, about 15 minutes.
Transfer the meatballs to a serving dish.
Serve garnished with the extra parsley.