Preheat oven to 350F.
Heat a large pan with half a cup of the olive oil, add the mushrooms, sweet potato, onion and zucchini, and saute until tender.
Add bacon and thyme, toss gently, and remove from heat.
Combine melted butter with remaining olive oil.
Unfold phyllo dough and place one sheet flat on a work surface with the short end closest to you.
Brush the dough lightly with butter-oil mixture and working quickly, slide another sheet of dough on top of the first, brush it with butter/oil mixture and repeat until you have 4 layers total on top of each other.
Cut the sheets of phyllo in half lengthwise to create long rectangular sheets. Facing the short end of each sheet, place 1/4 cup filling and a chunk of Bermuda Triangle on the end closest to you.
Starting at the filling end, fold the phyllo sheet up on the diagonal line. Fold the triangle of phyllo over straight and then diagonally again.
Continue folding first diagonally and then straight until you reach the end of the sheet.
The filling should be completely enclosed.
Repeat the process until all of the filling is used.
Arrange completed triangles on a parchment lined baking sheet, seam sides down. Brush with butter-oil mixture and sprinkle with salt and pepper.
Bake for 30 to 35 minutes, until the phyllo is brown and crispy. Serve warm.
Serves 4 to 6.