In a food processor, add the clams & oysters, shallot, egg white, heavy cream, dijon, salt, and pepper. Pulse until combined, but not pureed. Remove to a medium bowl and stir in the Panko breadcrumbs. Allow to rest for 20 minutes in the refrigerator.
Heat a large skillet over medium-high heat. Drizzle the pan with 1 tablespoon of olive oil. Add 4 - 2 1/2 inch cookie cutter rings to the pan and fill each with the clam mixture. Allow to cook for 4 minutes and carefully remove the rings with tongs and flip the cakes over. Continue to cook until the center is firm and no longer gelatinous, about 4-6 minutes longer. Remove to serving plates and assemble with the lemony greens and poached eggs, recipes follow.
Lemony Greens
In a medium bowl add the lettuce greens, lemon juice, olive oil, Manchego, salt, and pepper. Toss lightly with your hands to coat. Set aside.
Poached Eggs
Bring a large pot of water to a boil. Turn down to a simmer and add the vinegar. Using a slotted spoon, stir the water to make a whirlpool. Carefully break the eggs into the swirling water. The water should be slightly bubbling, not rapidly boiling. Allow the eggs to cook for 3 minutes (or longer to your taste). Remove with a slotted spoon to a plate while you assemble to clam cakes.
Assembly
Top each of the 4 clam cakes with 1 cup of the lettuce mixture. Top each with a poached egg and sprinkle with a pinch of crushed red pepper flakes. Serve immediately.