In a medium saute pan over medium heat, cook onions in 1 tablespoon butter until softened and translucent, stirring often, about 15 minutes. Do not brown. Remove from heat and cool to room temperature. Heat oven to 400°. Trim asparagus to 4-inch-long pieces; discard bottoms. If spears are more than ⅓ inch thick, slice in half lengthwise. Roll out Flaky Tart Dough to ¼-inch thickness. Line bottom and sides of a 9x9-inch tart pan (with removable bottom) with dough. Trim and discard excess. Layer onions on dough. On top of onions, place asparagus in two rows, tips pointing in, nestling as many as will fit neatly. Season with salt and pepper. Cut remaining 1 tablespoon butter into small pieces and scatter on top of asparagus. Bake 30 minutes. Remove from pan and slide onto a small cutting board. Using a vegetable peeler, slice cheese and place on tart. Serve warm.
Flaky Tart Dough
Place flour, sugar, and salt in a food processor fitted with a steel blade, and pulse to combine. Add butter and pulse a few times, until butter pieces are about the size of peas. Add half the water and pulse. Add remaining water, one tablespoon at a time, pulsing, just until dough comes together. Form a ball and wrap dough in plastic; place in refrigerator 20 minutes (or freeze up to 3 months). Yield: dough for 1 tart