Place chicken breasts into a large pot and cover with chicken broth; bring to a boil. Reduce heat to medium-low and simmer until no longer pink, about 20-25 minutes. Remove chicken, shred or chop, and keep broth hot.

Melt 3 tablespoons butter and olive oil in a large Dutch oven. Add potatoes, carrots, corn, celery, peas, and garlic. Sauté until veggies are soft, about 15 minutes. Stir in salt, black pepper, rosemary, nutmeg, thyme, and sage, and cook for 1 more minute.

Melt remaining butter. Sprinkle flour over veggies and stir constantly for 1 minute. Gradually add hot chicken broth, stirring until combined.

Stir in heavy cream and chicken. Season with salt and pepper. Cook, stirring occasionally, until thickened, about 20 minutes. Let cool for 5 minutes.

Preheat the oven to 375°F (190°C). Grease two 12-cup muffin tins. Line two baking sheets with foil and place the tins on top.

Pour chicken filling into muffin cups.

Roll out puff pastry and cut into 24 pieces slightly larger than the cups. Place over filling, brush with whipped egg, and season. Cut slits for venting.

Bake for 15-25 minutes until golden brown. Let cool for at least 5 minutes before serving.