Heat some extra-virgin olive oil, a turn of the pot, in a Dutch oven over medium to medium-high heat. Add the chopped speck and render a couple of minutes. Add the potatoes, celery, onion, garlic, chile, thyme, crab seasoning, salt, and pepper to the pot, cover, and cook 10 minutes, stirring occasionally. Add the chicken stock and milk and bring to a boil.
In a small skillet over medium heat, melt the butter. Whisk in the flour and cook the roux 1 minute, then stir in the mustard and transfer the roux to the chowder mixture. When the roux has incorporated, stir in corn and bring the chowder to a bubble, reduce to slightly thicken. Turn the heat off, cool completely, and store for make-ahead meal.
To serve, heat the oven to 425 degrees F. Unfold the pastry dough and choose the bowls or individual shallow casseroles or deep ramekins that you wish to serve in. Use one as a template and cut 4 shapes from the sheet of dough, using a sharp paring knife to maneuver around the dish shape. Arrange the pastry dough on a non-stick baking sheet or on a parchment-lined baking sheet. Beat the egg with a splash of water and brush the dough with the egg wash. Bake 10 to 12 minutes, or until golden.
Reheat the chowder, covered, over moderate heat until the soup bubbles, then uncover and simmer.
Meanwhile, run your hands through the crabmeat to check for shells, discard the the shells. Sprinkle the crab with hot sauce and stir into the chowder to heat through.
Serve the chowder in individual dishes topped with pastry.