Heat 2 Tbs. of the oil in a 10- to 12-inch skillet over medium-low heat. Cook the onion, mushrooms, and garlic, stirring frequently, until softened and just beginning to brown, 6 to 8 minutes.
Add the sherry, and simmer briskly, until almost dry, 4 to 5 minutes. Transfer to a large bowl and let cool until warm.
In a shallow dish that holds it in a single layer, soak the bread in the milk, flipping once, until soggy but not falling apart, 5 to 10 minutes, depending on the coarseness and freshness of the bread. Lightly squeeze a handful of bread at a time to remove some of the milk (it should be wet but not drenched). Finely chop and add to the bowl with the onion-mushroom mixture.
Position a rack in the center of the oven and heat the oven to 375°F.
Add the pork, veal, and eggs to the onion mixture. Scatter the rehydrated dried mushrooms, thyme, and sage over the meat, and then sprinkle with the Worcestershire, 2-1/4 tsp. salt, and 1/2 tsp. pepper. Use your hands to gently mix all the ingredients until just combined; try not to compact the mixture as you do this.
Heat the remaining 1 tsp. of oil in a small skillet over medium-low heat. Form 1 Tbs. of the meatloaf mixture into a small patty. When the oil is hot, cook the patty on both sides until cooked through, about 5 minutes total. Transfer to a plate and let cool slightly. Taste and adjust the salt, pepper, and other seasonings as needed. Repeat until you're satisfied with the flavor.
Line a 9x13-inch baking pan with parchment. Transfer the meatloaf mixture to the baking pan and form into a 10x4-inch rectangular block (it becomes loaf-shaped as it cooks). Spread the ketchup over the top and lightly down the sides of the meatloaf to glaze it.
Bake until an instant-read thermometer registers 160°F in the center of the meatloaf, 40 to 55 minutes.
Let the meatloaf rest for 10 minutes. Transfer to a cutting board or serving platter with a large spatula and cut into 3/4- to 1-inch-thick slices.