In a large skillet, bring water to a boil. Add asparagus; cover and boil for 3 minutes. Drain and immediately place asparagus in ice water. Drain and pat dry. In the same skillet, saute leeks in 1/4 cup butter for 5 minutes or until tender.
In a large bowl, combine the asparagus, leeks, cheese, eggs, lemon juice, parsley, mint, dill, almonds and cayenne.
Melt remaining butter. Place one sheet of phyllo dough on a work surface (keep remaining dough covered with plastic wrap and a damp towel to avoid drying out). Brush with butter. Repeat layers seven times. Spoon a fourth of the vegetable mixture along the short end of dough to within 1 in. of edges. Fold long sides 1 in. over filling. Roll up jelly-roll style, starting with a short side. Place seam side down on a greased baking sheet.
Repeat, making three more strudels. Brush tops with remaining butter. Bake at 350° for 40-45 minutes or until golden brown. Cool for 10 minutes before slicing.