Shred sharp white cheddar cheese into a medium bowl. Add mayo, mustard, paprika, salt, and diced pimentos to bowl. Stir together with a wooden spoon until mixture is completely combined. If you desire a creamier texture, add more mayo, as needed. Set aside and prepare the bacon jam.
Using kitchen shears, cut bacon into small pieces. Place sauce pan on stove and heat to medium. Add bacon pieces and cook until crispy. Remove from pan and drain on paper towels. Remove all but 1 tablespoon of bacon fat from saute pan.
Return pan to heat and set to medium low. Add diced onion and minced shallots to pan and cook until caramelized, about 15 minutes. Add garlic, brown sugar, maple syrup, apple cider vinegar, and cooked bacon to onion mixture. Bring mixture to a simmer and then reduce to low until consistency turns jammy and liquid reduces, about 8-10 minutes. Turn off heat.
Transfer pimento cheese and bacon jam to separate serving bowls. Serve alongside toasted white bread or butter crackers.