For the green beans almondine: Place a large pot of salted water over high heat and bring to a boil. Working in batches (to avoid crowding the pot and slowing the return a boil), cook the green beans for about 3 minutes, or until al dente. With a slotted spoon or tongs, transfer the green beans directly to an ice-filled bowl and shock to stop cooking. Drain well.
Heat the butter in a large skillet over medium-high heat until foaming and beginning to smell nutty. Add the blanched green beans and toss to coat. Add the toasted almonds and season with salt and pepper.
For the Mornay sauce: Melt the butter in a medium pot over medium heat. Sprinkle in the flour and mix with a wooden spoon to make a roux--it should look like wet sand. Cook, stirring, for a couple minutes and then whisk in milk. Bring to a simmer, stirring and scraping the bottom and scorners of the pan, and cook for a few minutes. Season with some salt, pepper and nutmeg. Remove from the heat and add the Gruyere, stirring until fully melted and combined.
For the crab-stuffed flounder: Preheat the oven to 375 degrees F. Melt the butter in a skillet over medium-high heat. Add the shallots, garlic and celery; cook until softened, 4 to 5 minutes.
Deglaze the pan with the vermouth and hot sauce to taste, and let cook for another minute. Pour the vegetables into a medium bowl and add the breadcrumbs, thyme and Old Bay; mix to combine. Gently fold in the crabmeat. Add salt and pepper to taste.
Rinse and pat dry the flounder fillets and lay on a baking sheet. Spread the stuffing along half of each fillet and fold over to enclose. Dot evenly with butter and sprinkle with salt and pepper. Bake until cooked through, 25 to 30 minutes
Set the stuffed flounder on serving plates and top with Mornay sauce. Serve with the green beans on the side.