Preheat oven to 400°F (204°C) with racks in top and bottom thirds.
Rinse mushrooms under cold water and pat dry thoroughly.
Twist off stems and discard or save for stock.
Scrape out dark gills from each cap with a small spoon.
In a bowl, combine goat cheese, garlic, bread crumbs, Parmesan, salt, shallot, and half the chives.
Mix until cheese is evenly distributed; mixture should hold together when squeezed.
Taste and adjust salt if needed.
Drizzle half the olive oil on a baking sheet and spread lightly.
Arrange mushroom caps gill-side up, spaced about an inch apart.
Spoon 2 teaspoons of filling into each cap, pressing gently.
Drizzle remaining olive oil over filled caps (about 1/4 teaspoon each).
Bake 18-22 minutes until caps are tender and topping is golden brown.
Let rest 2-3 minutes, then sprinkle with remaining chives and serve hot.
