Combine flour and salt in bowl. Cut butter into flour with 2 knives or in food processor until butter is size of peas. Drizzle in water and mix just until dough comes together.
Wrap in plastic wrap and chill 1 hour. Roll out dough into 13-inch circle on lightly floured surface.
Place in 12-inch tart pan. Fold any excess dough back into pan and press against sides. Place piece of foil or parchment paper on top of crust and fill with pie weights, rice or beans.
Bake at 375 degrees until edges barely begin to brown, about 20 minutes. Remove weights and foil or parchment paper.
Cut all but 1 inch of green tops off leeks. Split down middle and rinse very well. Cut into 1/8-inch-thick slices. There should be about 4 1/2 to 5 cups sliced leeks.
Melt 2 tablespoons butter in skillet over medium heat. Add leeks and season with salt to taste. Saute, stirring frequently, until soft and translucent, 8 to 10 minutes. Remove from skillet and set aside to cool.
Quickly rinse mushrooms in cold running water. If using morels, halve lengthwise. If using chanterelles or porcini, cut into 1/8-inch-thick slices. Saute mushrooms in remaining 1 tablespoon butter over high heat until most of liquid evaporates, about 3 minutes. Remove from skillet and set aside to cool.
Spread leeks in bottom of tart shell. Spread mushrooms over leeks. Cover with grated cheese. Place on baking sheet or piece of foil. Bake at 400 degrees until cheese begins to melt, 10 to 15 minutes. Remove from oven.
Trim each asparagus spear to 5 1/2 inches. Place asparagus spears on top of cheese like spokes of wheel. Place cherry tomatoes in decorative fashion, cut-side up, on cheese. Lightly spray with cooking spray. Season to taste with salt.
Bake at 400 degrees until cheese is bubbly and asparagus is tender, about 15 minutes.
If you can't find fresh morels, soak dried ones in hot water until they regain their shape.