In a medium bowl, combine the torn bread and ¼ cup of bourbon. Let it soak until the bread absorbs the liquid.
Add the ground beef, ground pork, eggs, tomato paste, salt, and pepper to the soaked bread. Mix gently by hand until everything is just combined—don’t overmix.
Roll the mixture into 18 to 20 balls, about 1½ tablespoons each.
Heat 4 tablespoons of olive oil in a large cast-iron skillet over medium-high heat. Add the meatballs in batches and cook, turning often, until browned on all sides. Transfer to a paper towel–lined plate to drain.
In a medium Dutch oven, heat the remaining tablespoon of oil over medium-high heat. Add the onion and garlic, and cook until golden brown and fragrant.
Stir in the chili sauce, apple jelly, molasses, and the remaining ¼ cup of bourbon. Cook, stirring occasionally, until the sauce starts to bubble.
Reduce the heat to medium-low. Add the browned meatballs to the sauce and simmer, stirring occasionally, until the meatballs are heated through and coated in the glaze.
Serve warm as an appetizer or over rice or mashed potatoes for a full meal.