Yield: approximately 3 dozen
1¼ cups butter, divided
2 tablespoons olive oil
2 yellow onions, thinly sliced
1 teaspoon sugar
1 (10-ounce) package goat cheese, softened
1 (8-ounce) package cream cheese, softened
1 (8-ounce) package sharp white Cheddar cheese, shredded
1 tablespoon chopped fresh thyme
1 teaspoon salt
1 teaspoon ground black pepper
½ (16-ounce) package frozen phyllo dough, thawed
1. Line 2 rimmed baking sheets with parchment paper; set aside. In a medium cast-iron skillet, add 1⁄4 cup butter and olive oil. Melt butter over medium-high heat. Add onion and cook, stirring often, until tender, approximately 5 to 8 minutes. Stir in sugar, and continue to cook, frequently scraping browned bits from the bottom of pan, until onion is translucent and golden brown, approximately 18 to 20 minutes. Remove from heat, and let cool completely.
2. Preheat oven to 375°.
3. In a large bowl, beat goat cheese and cream cheese at medium-high speed with an electric mixer until smooth and creamy, approximately 4 minutes. Add onion, Cheddar, thyme, salt, and pepper, beating to combine. Set aside.
4. Melt remaining 1 cup butter in microwave or in a saucepan.
5. On a clean, flat work surface, unroll phyllo dough. Cut stack of dough lengthwise into 3 equal strips. Place dough on one half of a damp towel, and fold remaining half over dough to prevent drying.
6. Working with 2 strips of phyllo at a time, brush each strip with melted butter. Stack strips, and spoon approximately 1 teaspoon cheese mixture onto one end of stack, leaving a 1-inch border at end. Fold corner of phyllo over filling to form a triangle. Continue folding back and forth (flag style) until end of stack is reached. (Be careful not to fold too tightly, or triangles will burst during baking.) Repeat procedure with remaining phyllo strips, melted butter, and cheese mixture.
7. Place triangles, seam side down, on prepared baking sheet. Lightly brush tops with melted butter. Bake until golden brown, approximately 20 minutes. Serve warm.