Position a rack in the center of the oven and heat the oven to 350°F.
Heat 1 Tbs. of the oil in a 10-inch skillet over medium heat. When hot, add the onion and cook, stirring frequently, until softened, 3 to 5 minutes. Transfer to a plate to cool.
Put the ground beef, veal, and pork in a large bowl and gently knead them with your hands until just combined. Add the cooled onion, paprika, 2 tsp. salt, and 1 tsp. pepper and gently knead to blend. Add the remaining ingredients (except for the remaining vegetable oil) and gently knead with your hands or stir with a large spoon until just incorporated.
Wipe out the skillet and heat the remaining 1 tsp. oil over medium heat. When the oil is hot, add a quarter-size piece of the meat and cook, turning halfway through cooking, until the meat is cooked through, about 1 minute on each side. Cool briefly and taste. If it’s too moist to hold together, add up to 1/2 cup more breadcrumbs to the meat mixture; if it’s too dry, add an extra egg. If necessary, add salt and pepper. Repeat cooking quarter-size pieces of the meat until you’re satisfied with the flavor and consistency.
On a parchment-lined rimmed baking sheet, mold the meat mixture into a 9x5-inch loaf. Bake until the meat is firm to the touch and has an internal temperature of 160°F, about 1 hour. Allow the meatloaf to rest for 15 to 20 minutes before serving.
You can shape the raw meatloaf up to 1 day ahead. Refrigerate it overnight to meld the flavors for a tastier meatloaf the next day.