Make the pickles the day before. Place sliced cucumbers in a bowl and coat with kosher salt. Allow to sit for 30-40 minutes. Drain and pat dry.
Place the fresh dill and garlic into a pint sized jar. Add the salted cucumbers to the jar.
In a small sauce pot, heat the vinegar, water, sugar and spices until the sugar is completely dissolved.
Pour the warm pickling liquid over the cucumbers in the jar. Allow to sit at room temperature until cooled. Refrigerate.
For the mayo, crack egg yolk into a bowl. Squeeze over a few drops of lemon juice and add a pinch of salt. Whisk constantly while slowly incorporating the oil. Start slowly with a few drops at a time. You can increase speed as the mayo comes together.
Add vinegar, lemon juice and salt, to taste. Add a few drops of water to thin out the mayo, if needed. Refrigerate. This can also be made a day ahead.
For the onions, heat the grill to medium-high. I used an indoor grill pan. Coat the onions in extra virgin olive oil and season with salt.
Grill for about 3 minutes per side or until softened and charred in spots. Keep grill warm.
Brush buns lightly with oil. Add buns to the grill, cut side down and toast about 30 seconds or until grill marks form. Turn grill up to high. Grease grates with oil.
For the burgers, shape meat into 4-6oz patties, about the width of the buns. Make a slight indentation on the top of each burger to allow for expansion.
Season liberally with salt and pepper. Place on grill. Grill about 2- 2 ½ minutes per side for medium-rare and an additional 1-2 minutes for medium. Burgers can also be cooked in a nonstick or cast iron pan.
After flipping, place two slices of cheese on each burger. If using a grill pan, splash a little water on the grill and cover the burger with an inverted bowl for the remainder of the cooking process to melt the cheese.
To construct the burger, spread the bottom bun with mayo. Cover with a piece of lettuce. Add the cheeseburger. Top with grilled onions, sliced tomatoes (seasoned with salt) and pickles. Add ketchup, if desired, add the top bun and enjoy!