In a skillet on medium-high heat, add olive oil. Saute onion and garlic until fragrant. Add in brown sugar. Cook another 2-3 minutes until onions are softened. Add in paprika and cook well. Stir in cider, ketchup, and salt and pepper to taste. Check for seasonings- adjust salt and pepper if needed. Set aside in a small serving bowl.
In the same skillet, add another tbsp of olive oil. Add bacon pieces and cook until crispy. Add in shallot and smoked paprika. Cook until shallots are tender- about 3-4 minutes. Drain on paper towels.
In a large bowl, season beef with salt and pepper. Once the bacon mixture is cool enough to handle, mix it into beef. Carefully form patties, but do not pack beef too tightly. Grill for 4-5 minutes on each side until the internal temp is at least 160 degrees or more if you prefer a well-done hamburger. Top with a sharp cheddar. Serve with BBQ sauce and toasted buns.