Whisk two tablespoon of lemon juice with 1/3 cup of olive oil and sea salt in a small bowl. Add the thinly sliced onions and toss to coat and set aside.
Preheat the grill to medium or heat a grill pan on the stove top over medium-high heat. With a pastry brush, lightly brush both sides of each slice of bread with Primo Favolosa EVOO. Place the bread on the grill and toast until light golden brown and grill marks appear, flipping once during the process (take care not to burn the bread).
While the bread is still very warm, rub the cut garlic clove over both sides of the bread slice. Allow the bread to cool completely, then begin layering by adding a slice of avocado. Brush the sliced avocado with a small amount of the onion-lemon-olive oil mixture, and a grind of fresh pepper. Add the smoked salmon, and top with a few slices of marinated onions and a sprinkle of chopped parsley.