Place the oil and 1 Tbsp. of the butter in 10-inch cast iron or other ovenproof skillet and set over medium heat. When the butter is melted, and the onion and garlic and cook until tender, about 5 to 6 minutes. Remove onions from the skillet and set on a plate.
Set the skillet back on the heat and add the remaining 2 Tbsp. butter and the vinegar. Cook just until the butter melts. Remove skillet from the heat and set on a work surface.
Set and overlap 2 of the tomatoes slices in the centre of the skillet. Now arrange and overlap the remaining slices of tomatoes in a ring around the ones in the centre. Spread the onions on top of the tomatoes, and then season with salt and pepper.
Preheat the oven to 425°F. Place the puff pastry on a lightly floured surface. Roll into a circle that’s 1" wider in diameter than the skillet. Carefully fold the pastry in half and lay it across the centre of the skillet. Carefully unfold the pastry to completely cover the tomatoes.
Bake the tarte tatin in the middle of the oven for 30 minutes, until the pastry is puffed and golden. Let tart stand at room temperature for 15 minutes.
Place a round platter (or board) over the skillet. Hold skillet and platter firmly together and invert, releasing the tarte tatin onto platter. Serve the tarte warm or a room temperature; topped with the oregano leaves, to taste, and the cheese.
Note: Puff pastry is sold in our Frozen Foods Department. The tomatoes slices used in this recipe were about 1/4" to 1/2" thick, and 2 1/2" to 3" wide. You’ll need three medium to large tomatoes to get the slices required for this recipe.