Snap off the ends of the asparagus and rinse. Place into a large pan and pour in enough water to almost cover. Cover, with the lid vented. Place over medium heat until the water begins to boil. Close the lid completely and turn down the heat. Steam for 2-5 minutes, until bright green and tender-crisp. Take off the heat and drain.
Open the package of phyllo dough and lay onto a flat surface. Cover with plastic wrap and place a damp paper towel or wash cloth on top.
Pulse the walnuts in a food processor until coarsely chopped.
Heat the oil in a small sauce pan over medium heat for 3 minutes, until hot. Preheat the oven to 375 and grease a baking sheet.
Take a sheet of phyllo dough and brush with oil. Place another sheet on top and brush again. Make it 3-4 layers thick.
Take 3-4 asparagus stalks and stack them in a pyramid at the end of the phyllo dough that is closest to you. Sprinkle with walnuts, and a bit of the pepper, salt, garlic powder and tarragon.
Begin to roll it all up in the dough. Stop after every rollover and brush the dough with more oil, and close the ends up as you roll. It should resemble a large egg roll. Seal up the end of the sheets with oil and place on the greased pan. Brush the top with oil so it doesn’t dry out.
Repeat this with the dough and asparagus until it is all used up. Bake for 15-20 minutes, until golden brown. Let cool for a few minutes and slice diagonally into thirds. Serve over a salad, or arranged on a platter as an appetizer.