In large skillet heat butter until melted and foaming. Add onions and celery. Season to taste with salt and pepper. Cook three 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 in half-and-half. Lightly beat eggs.
In large mixing bowl combine ground meats, bacon, cooled vegetables, and bread crumb mixture. sprinkle the 1-3/4 teaspoon of 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.
For Ketchup Topping: Combine ketchup, brown sugar, and vinegar. Spoon over top of loaf. Bake on middle rack for 1 hour or until meat thermometer reaches 155°F Let rest 10 minutes.