Combine sugar, vinegar and water in a sauce pot and bring to a boil. Remove from heat and add cucumber slices. Refrigerate for an hour before use, the cucumbers will be tender yet still have texture.
Combine Brussels sprouts, mayonnaise and garlic paste in a mixing bowl; keep refrigerated until use.
Heat oil in a large skillet over medium. Add onions, butter and cook on medium-low heat for 30 minutes, stirring often until onions are tender. Drain and reserve excess butter to toast bread slices, refrigerate onions until cooled.
Heat 1 tablespoon of reserved onion butter in the same skillet over medium. Toast 2 slices of bread at a time until desired doneness, repeat with remaining ingredients and set aside.
In the same skillet, heat the tomato slices until a slight charring occurs, set aside.
Combine the sausage and caramelized onions together in a mixing bowl. Divide the sausage mix into 4 equal parts and roll into individual ball-shapes. Using the same skillet, smash the sausage into the skillet with a flat spatula until you have your desired thickness. Cook over medium heat for 12-15 minutes or until the natural juices run clear. Finish with the shredded cheese and let melt before removing from the skillet. You can cook them all in the same skillet or two at a time. Layer the burger between toasted bread with tomatoes, pickles and slaw. Enjoy!