Heat a large sauté pan over medium heat, add the olive oil and heat through. Add the butter and allow to melt then add the onions and cook, stirring frequently until the onions are soft and translucent, about 6 minutes.
Reduce the heat to medium-low and cook, stirring occasionally until pale golden brown, about 15 minutes. Add the salt and sugar and continue to cook, stirring occasionally until deep brown and caramelized. Remove from heat and set aside to cool.
In a large mixing bowl combine the ground beef, caramelized onions, cheddar cheese, pretzels and remaining salt. Use your hands to combine the mixture, being careful not to over-mix.
Line a baking sheet with wax paper and set aside then fill a small bowl with water to help seal the dumplings. To fill the dumplings, work one at a time. Lay one dumpling wrapper in the palm of your hand and use a finger to wet the edge of the wrapper with water. Scoop 1 tablespoon of filling into the middle of the wrapper. Fold the dumpling in half (like a taco) by bringing up the bottom to meet the top, pinching to seal it.
While firmly holding the seam with your thumb and index finger, use your index and the middle finger of your other hand to fold a portion of the wrapper towards the center of the seam to create your first pleat. Once the dumpling is fully sealed, place it on the wax paper-lined baking sheet and cover with plastic wrap to keep from drying out. Repeat with the remaining wrappers and filling.
To fry the dumplings, heat a large sauté pan over medium heat, add the oil and heat through. Arrange the dumplings in a circle in the pan and fry the bottom of the dumplings without moving them. Once the dumplings easily release from the bottom of the pan they are ready to steam.
Add 1/3 cup of water to the pan and tightly cover with the lid. Let steam until the meat is cooked through and the dumpling is tender, about 5 to 6 minutes. Uncover and continue cooking until all water has evaporated.
Remove from the pan and serve immediately with the sauce and chives.