Slice onion into strips. Mince a few strips until you have 2 tablespoons. Set minced onion aside.
Add 1 tablespoon to large saute pan and set to medium heat. Add sliced onions, sugar, and a pinch of salt. Cook for about 10 minutes. Add 2 tablespoons of water to help get the onions a little mushy. Cook until water has evaporated. Remove from heat.
While onions cook, mix ground pork with minced onions, paprika, half of minced garlic, and about 1/4 teaspoon of salt. Form into to patties. Heat another saute pan over medium heat with a large drizzle of olive oil. Once hot, add patties and cook for 7 minutes. Flip patties and cook for 4 more minutes. Turn off heat.
Add one slice of cheese to eat patty. Cover for 1 minute or until cheese is melted. Remove from saute pan and place on bottom half of bun. Top with caramelized onions.
In a small dish, add sour cream, mayo, other half of minced garlic, salt, and pepper (to taste). Stir to combine. Spread onto top half of hamburger bun. Top burger with top bun. Serve immediately.