Heat oil in a large skillet over medium-high heat.

Add mushrooms, shallots, salt and pepper; cook, stirring frequently, until mushrooms are very tender and have released their liquid, about 10 minutes.

Stir in thyme. Set aside to cool.

Preheat the oven to 400°F.

Line a large baking sheet with parchment paper.

Stir in thyme. Set aside to cool.

Preheat the oven to 400°F.

Line a large baking sheet with parchment paper.

Lay 2 phyllo sheets on a work surface with long side facing you. (Keep remaining phyllo covered with plastic wrap or a damp kitchen towel to prevent it from drying out while you work.)

Brush sheets lightly with butter.

With a sharp knife, cut each piece of phyllo in half lengthwise, then across 4 times to make 10 rectangles, each about 6 1/2 inches long and 3 3/4 inches wide.

Place a piece of Brie toward one end of each piece and top with 1 tablespoon mushroom mixture.

Fold long ends of phyllo in to cover sides of filling, and then roll cheese up in phyllo as if you were rolling a mini burrito.

Place seam-side down on a baking sheet.

Repeat with remaining phyllo, mushroom mixture and Brie, making 30 bites.

Brush bites with remaining butter and bake until phyllo is browned and very crisp, 25 to 30 minutes.

Serve warm.

Note: These hors d’oeuvres can be made up to 1 month in advance. Form as directed, but instead of baking them, place prepared baking sheet in the freezer. When frozen through, 1 to 2 hours, transfer the bites to freezer-safe resealable plastic bags, remove excess air and seal. Bake them straight from frozen on a parchment-lined sheet as directed, adding about 5 minutes to the baking time.