If you have whole clams, shuck them. Remove the foot and adductor muscles, then rub all the meat with a handful of fine sea salt for one minute. Rinse the meat thoroughly in ice water and pat it dry. Finely dice the clam meat to get about 1 cup.
Bring the vinegar, water, sugar, and salt to a boil. Pour the mixture over the sliced peppers and let it sit at room temperature for at least 2 hours. This can be done up to a week in advance and stored in the refrigerator.
Peel, seed and finely dice the cucumber. Toss it with a few tablespoons of the Champagne vinegar. Let it sit for 15-20 minutes while you prepare the other ingredients.
In a bowl, gently toss the diced clam meat with the juice from half a lime, the olive oil, and flaky sea salt to taste.
On a large platter or in a bowl filled with crushed ice, arrange the nasturtium leaves. Divide the seasoned clams evenly among the leaves. Top each clam with a few pieces of the pickled cucumber, one slice of pickled aji dulce pepper, and one edible flower petal.
Serve the dish cold, with additional lime wedges and flaky sea salt on the side for your guests to add as they wish.