Melt butter in a 4-qt. saucepan over medium-high heat. Add garlic, onion, carrots, parsnips, mushrooms, celery and thyme. Cook until the carrots and parsnips are tender, about 10 minutes. Add sherry and cook for 5 minutes until reduced. In a large, glass measuring cup, heat the half and half in the microwave for 3-4 minutes until it is very hot. Lower the heat to medium and whisk the flour into the onion mixture, stirring well. Cook for 2-3 minutes until the flour starts to pull away from the pan. Add the hot half and half and bring the sauce to a boil. Cook, stirring constantly, until the sauce is slightly thickened, 3–4 minutes. Stir in lobster, nutmeg, salt, pepper, lemon juice and peas.

Heat oven to 425°. Divide lobster mixture between four 8-oz. dishes set on a foil- covered baking sheet. On a lightly floured surface, roll pastry into a 14″ square and cut it into four squares or circles about 4 “ around using a saucer as a template. Place one square of puff pastry over each dish and press to seal it tight around the edges. Cut four small vents into the top of each pastry. Brush pastry with egg; bake until golden on top, about 30 minutes.