For the vinaigrette: Place sugar and water in a medium nonreactive saucepan over high heat and bring to a boil. Continue boiling until sugar has completely melted. Reduce heat to low, add the lemon wedges and cook slowly until almost soft. Remove with a slotted spoon and place on a baking rack. Let dry at room temperature overnight.
Place lemon juice in a small nonreactive saucepan and cook until reduced to 1/4 cup, let cool.
Place cooled lemon syrup, sherry vinegar, shallots and garlic in a blender and blend until smooth. With the motor running, slowly add the olive oil and season with salt and pepper. Pour into a bowl and fold in the parsley.
Fry capers in oil until crisp, about 1 1/2 minutes. Drain on paper towel.
For the potatoes: Preheat oven to 350 degrees F. Toss the potatoes with the oil and season with salt and pepper to taste. Arrange the potatoes in an even layer in the bottom of 4 small cazuelas. Place in the oven and bake 3/4 of the way through.
For the salmon: Remove the potatoes from the oven and reduce the heat to 250 degrees F. Lightly brush the salmon on both sides with olive oil and season with salt and pepper to taste. Place the salmon on top of the potatoes and return the cazuelas to the oven. Bake for 12 to 14 minutes, until cooked through. Remove from oven and immediately drizzle with lemon vinaigrette, and sprinkle with chopped parsley and capers.