In a small bowl, combine 1 1/2 tablespoons of very finely minced shallot, 1 tablespoon of finely minced cucumber, 3 tablespoons of champagne vinegar, and 1/3 cup of champagne. Add a pinch of freshly cracked black pepper and kosher salt. Stir well to blend all the flavors, then let the mixture sit at room temperature for at least 1 hour.

Begin by rinsing the fresh oysters under cold water, using a brush to remove any dirt or grit from the shells. Prepare an oyster knife and a towel for grip and safety. Carefully insert the knife into the hinge of each oyster, twisting gently to pry it open. Retain the oyster in its bottom shell while discarding the top shell. As you shuck, arrange the oysters on a tray filled with ice.

Once all the oysters are shucked, arrange them attractively on the ice-filled tray. Serve the oysters alongside the prepared champagne mignonette for dipping. Garnish with lemon wedges.