Preheat oven to 375 degrees.
Wash the asparagus and cut off the bottom of the stems that are greenish-white and tough. Bring a pot of water to a boil, add 1 tablespoon salt, submerge the asparagus for 30 seconds to blanch, remove the asparagus from the pot and quickly submerge in iced water to shock. Set the asparagus aside.
From the wild leeks, trim off the dirty roots and snip an inch off the tops, before washing them carefully in cold water. Heat a saute pan over medium heat with 1 tablespoon of butter. When the butter begins to foam add the wild leeks, season with salt and pepper, and cook gently for 3 to 4 minutes. Add the broth to the wild leeks and simmer until all of the broth has evaporated but be careful not to burn the leeks. Remove from the saute pan and allow to cool.
Prepare a space to work with the phyllo dough: unwrap the dough and cover with a cloth, have a brush and the olive oil ready and have a cookie sheet ready on which the tart will be baked. Begin by lightly brushing the center of the cookie sheet with a film of olive oil. Next, lay the first sheet of dough on the cookie pan, brush the dough lightly with oil and overlap width wise the next sheet over only half of the first so that now the two sheets make a pastry sheet 50 percent wider (not longer) than the original dimension of the pastry. Don't be concerned if the lengthwise ends of the dough are overflowing from the edges of the pan: all of the edges of the dough will be rolled up to form the edges of the tart.
Brush the second sheet of dough with oil and lay another sheet squarely over the first so that in alternating this pattern you build your wide pastry base. Continue to alternate the dough sheets, brushing each layer with oil, until you have used half the package of dough.
Gather the edges of the phyllo between the tips of your fingers and begin to roll them toward the
center to form the sides of the tart. Roll uniformly inward until the rolled edge is even all around and the round tart resembles a pizza. Leave a pastry base of 10 to 12 inches into which the vegetables and cheese will go after the tart shell is blind baked.
Place the empty tart shell into the oven and bake for 6 minutes. Remove the pastry from the oven and allow to cool for 10 minutes before filling. This pastry preparation can be done over the course of several hours and can even be done a day or two ahead if the blind baking is reserved until the last moment and the raw pastry is covered with plastic wrap and refrigerated.
To fill the tart crumble the goat cheese and spread it evenly over the base of the tart. Next add an even layer of wild leeks, followed by the asparagus which should be fanned, tips out, from the center of the tart. Season the tart lightly with salt and pepper, place into the 375 degree oven and bake for 15 minutes or until the cheese has softened and the crust becomes a rich golden brown. Serve immediately.
While the tart is baking (or ahead of time if possible) prepare the vinaigrette. Place the red pepper, mustard, vinegar and 1/4 teaspoon salt and black pepper in a food processor. Pulse to chop the red pepper to a fine dice. When the pepper has been pulsed enough, begin to drizzle in the walnut oil to create an emulsified dressing.
Serve the tart with a small green salad and a drizzle of red pepper vinaigrette.