To make the clam cakes: If using clams in their shells, combine the clams and water in a large skillet. Bring to a boil, reduce heat to a simmer, then cover. Steam for 3 to 4 minutes, or until the shells open. Discard any clams that do not open. Remove from heat and let the clams cool in their shells. Take the meat out of the shells. Strain the clam juice, reserving 3/4 cup. Coarsely chop the clam meat. This will produce approximately 1 1/4 cups of chopped meat. If using jarred clams, drain well, reserving 3/4 cup of the juice.
In a medium bowl, combine the chopped clams, bell pepper, parsley, and tarragon; set aside.
In a large bowl, combine the all-purpose flour, semolina flour, baking powder, cayenne pepper, and salt. In a medium bowl, whisk together the milk, reserved or bottle clam juice, egg yolks, melted butter, and lemon juice. Stir the liquid ingredients and clam mixture into the dry ingredients to form a batter; set aside.
In a large bowl, beat the egg whites until stiff, glossy peaks form. Fold them into the batter. Let the batter stand for 15 minutes.
In a large nonstick skillet, heat 2 teaspoons of the oil over medium heat. Spoon in about 3 tablespoons of the batter for each clam cake (about 4 per batch). Cook, turning once, until lightly browned on each side, about 3 minutes total. Place the cakes on a plate in a low oven to keep warm. Repeat the process, adding more oil as needed, until all the batter is used. Serve hot with tartar sauce.
To make the tartar sauce: In a medium bowl, combine all of the tartar sauce ingredients and stir to blend. Cover and refrigerate until ready to use. This sauce can be made up to 2 days ahead.