1. In a large skillet set over medium-high heat, add the olive oil. Add the onion, red and yellow peppers and the eggplant and cook, stirring frequently, until the vegetables are softened and caramelized, about 10 minutes. Stir in the garlic and cook until fragrant, about 1 minute, then remove the pan from the heat and transfer the vegetables to a large bowl. Crumble the feta on top of the mixture, stir in the thyme leaves and season with salt and pepper. Refrigerate until cooled.

2. Preheat the oven to 450°. Place the phyllo dough on the counter, unfold and cover with a damp kitchen towel or paper towels. Set one sheet of phyllo on a cutting board and use a pastry brush to coat the entire sheet with a thin layer of melted butter. Fold the bottom of the sheet in half lengthwise (to make a long, thin horizontal rectangle) and butter again. Fold in half from left to right (like a book) and butter the top sheet. In the center of the folded phyllo, place 3 tablespoons of the vegetable-feta mixture. Tuck in both of the long, vertical edges and roll the dough up from bottom to top. The finished cigar should be about the size of a spring roll. Place on a rimmed baking sheet and brush with more melted butter. Repeat 11 times or until the vegetable-feta mixture is gone.

3. Bake until golden brown, about 7 to 8 minutes. Gently turn the boreks over and bake until the other side is golden brown, an additional 3 to 4 minutes. Serve warm.