Slice the lemons into ¼ inch slices and remove the seeds. Peel the garlic cloves and leave them whole.
Place a cast iron skillet over high heat. Add 1 tablespoon olive oil to the pan, when the pan is heated add the lemon slices in batches making certain to not cool the pan down.
Cook the lemon slices until they are charred dark brown and turn them in order to cook the other side. Add the garlic cloves to the pan and cook them until brown on both sides.
Clean and slice the green onions. Add them to the pitcher of a blender or the bowl of a food processor along with the remaining ingredients including the white wine vinegar, sugar, salt, pepper, Dijon mustard, and olive oil.
Once the lemons are cooked to a dark brown along with the garlic cloves, place them into a small bowl to cool down for 4-5 minutes.
Add the garlic and lemon slices to the blender pitcher or food processor bowl and combine on medium-high speed until blended and creamy.
Taste the dressing and season to taste with more salt and pepper, or even a bit of fresh lemon juice. Place the dressing into a container with a tight-fitting lid and store in the refrigerator.