For the puff pastry:
Preheat the oven to 400 degrees F.
Roll the puff pastry out to 1/8-inch thick. With a 4-inch round cutter, cut out 16 circles. Using a 2 1/2-inch cutter, cut the centers out of 8 of the circles. Place the whole circles on a parchment lined baking sheet.
In a small bowl, beat the egg with the milk to make an egg wash. Brush the whole circles with the egg wash. Lay the circles with the center cut out on top of the whole circles.
Place in the oven and bake for 10 minutes, or until golden brown. Remove from the oven and cool.
In a large, heavy saucepan, heat olive oil over medium heat. Add onions, celery, garlic, corn, peas, bay leaf, and thyme and cook until vegetables are soft, about 6 minutes. Season with salt and pepper, to taste. Add mushrooms and saute for another 2 minutes. Add stock, red pepper flakes, if using, hot sauce, and Worcestershire sauce and bring to a boil. Season, to taste, with salt.
Meanwhile, make a slurry by combining the flour and water. Add the slurry and bring to a boil. Add lobster, lemon juice, green onions, if using, and parsley and cook at a simmer for 5 minutes, stirring occasionally. Add butter and stir to combine well. Taste and adjust seasoning, if necessary.
Serve lobster mixture in the puff pastry, garnished with chopped chives.