To prepare pasta, combine saffron and 1/4 cup water in a saucepan. Cook over low heat 10 minutes; cool. Lightly spoon flour into dry measuring cups; level with a knife. Combine 1 1/2 cups flour and salt in a bowl. Make a well in center of mixture; add 3 tablespoons saffron water, 1 tablespoon oil, and eggs. Stir to form a dough. Turn dough out onto a lightly floured surface; shape into a ball. Knead until smooth and elastic (about 10 to 15 minutes); add remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands. Dust dough lightly with flour, and wrap in plastic wrap. Chill 1 hour.
Divide dough in half. Working with 1 portion at a time, pass dough through smooth rollers of pasta machine on the widest setting. Continue moving width gauge to narrower settings; pass dough through rollers once at each setting, dusting with flour, if needed. Repeat procedure with remaining half of dough. Cut dough portions into 8 x 1-inch strips. Hang pasta on a wooden drying rack (no longer than 30 minutes).
To prepare mushroom broth, melt 1 tablespoon butter in a saucepan over medium heat. Add porcinis and next 7 ingredients (porcinis through bay leaf); cook 5 minutes. Add broth; bring to a boil. Reduce heat to medium-low; simmer until reduced to 1 1/4 cups (about 25 minutes). Strain broth through a sieve into a bowl; reserve 3/4 cup broth. Discard solids.
Cook pasta in boiling water 2 minutes or until al dente; drain.
Heat 1 tablespoon oil in a nonstick skillet over medium-high heat. Add shallot, mushroom caps, and minced garlic; cook 3 minutes. Add reserved 3/4 cup broth; reduce heat to medium, and cook 3 minutes. Stir in asparagus, peas, chives, and 1/2 teaspoon butter. Add cooked pasta; toss to coat. Sprinkle with cheese.