Preheat the oven to 350 degrees F. Bake the shells according to the package directions. Let cool while you make the filling.
Heat a skillet over medium heat and add the butter. When the butter is melted, add the shallots and garlic, and cook until soft, about 5 minutes. Add the mushrooms and season with salt and pepper, to taste. When the mushrooms have released their liquid, add the wine and thyme and cook until most of the liquid has evaporated, about 5 minutes.
Cut the Brie into 15 small pieces. Divide the mushroom mixture among the phyllo shells. Top each with a piece of the cheese. Return the shells to the oven and bake until the cheese has melted, about 5 minutes. Transfer the bites to a serving platter. Garnish with chives and serve warm.