In a large saute pan, heat oil over medium-high heat. Add the onion and cook, stirring occasionally for about 10 minutes, or until onion begins to soften. Remove from heat and set aside to cool.
Dust a clean work surface with flour and roll the puff pastry dough to 1/8 inch thick and about 9X11 in size. Place the dough on a parchment-lined baking sheet.
Top the dough with the onions, leaving - inch space at the edges. Fold the 1-inch edge in half to create height along the edge of the tart. There should now only be 1/2 inch of space along the edge.
Line up the asparagus on top of the onions with the tomatoes. Whisk the eggs well and pour over top of the asparagus. Sprinkle with feta cheese.
Bake for 25 minutes, or until the pastry is puffed and golden. Remove the tart from the oven and sprinkle with salt and pepper. Let the tart cool for a few minutes before cutting into 6 pieces.