In a large skillet, add the olive oil and butter, cook over medium-high heat. Add the onions and 1/4 teaspoon each of salt and pepper. Cook, stirring every so often, until the onions begin to soften and caramelize, about about 15 minutes.
Add the sliced mushrooms and thyme, continue cooking until the mushrooms are soft, about five minutes. Stir in the wine and cook until evaported. Remove from the heat.
Preheat oven to 350 degrees F.
Roll out the puff pastry sheets and cut each sheet into 9 squares (18 squares total). Place squares on a piece of wax paper or parchment paper (this will prevent sticking).
Divide the mushroom mixture among the 18 squares, top with havarti cheese. Don't overfill or else it will be very difficult to seal edges.
Brush egg wash around the perimeter of each pastry square and carefully fold dough over filling to create triangles, pinching edges closed to create a good seal.
Generously brush the top of each turnover with egg wash, sprinkle with sesame seeds. Place on a parchment paper lined baking sheet.
Bake for 15 to 20 minutes or until lightly golden. Serve immediately with a sprinkle of chopped fresh thyme and flaky sea salt.
Notes
*The turnovers can be made in advance and either frozen or left in the fridge for up to 3 days. Bake as directed. If baking from frozen, bake 5 minutes longer.