Preheat oven to 350 degrees F. In large skillet heat butter until melted and foaming. Add onions, mushrooms, and celery. Season to taste with kosher salt and black pepper. Cook 3 minutes, being careful not to brown.
Sprinkle thyme over onion mixture. Rub garlic and pinch of salt into paste; add garlic. Cook and stir until onions are tender and translucent. Stir in grated carrot; remove from heat. Cool completely. Meanwhile, soak bread crumbs in half-and-half; lightly beat in eggs.
In large mixing bowl combine ground meats, bacon, cooled vegetables, and bread crumb mixture. Sprinkle the 1-3/4 teaspoons salt and the pepper. Using hands, mix until well blended.
Turn mixture into rectangular baking dish. Using hands, shape into a 9x5-inch loaf. Make shallow indentation around sides.
Combine ketchup, brown sugar, and vinegar. Spoon over top of meat loaf. Bake on middle rack for 1 hour or until meat thermometer reaches 155 degrees F. Let rest 10 minutes before slicing.