1. To prepare filling, combine the first 8 ingredients in a bowl. Cover and refrigerate 1 hour.
2. To prepare pasta, weigh or lightly spoon flour into dry measuring cups; level with a knife. Place flour and 1/4 teaspoon salt in a food processor; pulse 3 times or until blended. With processor on, slowly pour water and eggs through food chute; process until dough forms a ball. Turn dough out onto a lightly floured surface; knead until smooth and elastic (about 5 minutes). Wrap dough in plastic wrap; refrigerate 30 minutes.
3. Divide dough into 8 equal portions. Working with 1 portion at a time, pass dough through smooth rollers of pasta machine on widest setting (cover remaining dough to keep from drying). Continue moving width gauge to narrower settings; pass dough through rollers once at each setting, dusting with flour if needed. Lay pasta sheet flat on a lightly floured surface; cover. Repeat procedure with remaining dough.
4. Spoon 1 1/2 teaspoons filling mixture at about 2-inch intervals along the length of 1 pasta sheet. Moisten edges and in between each filling portion with water; place 1 pasta sheet on top, pressing around filling to seal. Cut pasta sheet into 6 (3 x 3-inch) ravioli, trimming edges with a sharp knife or pastry wheel. Brush excess flour from ravioli. Place ravioli on a lightly floured baking sheet (cover to prevent drying). Repeat procedure with remaining dough portions and filling mixture to form 24 ravioli.
5. To prepare sauce, heat oil in a large skillet over medium heat. Add shallots and next 3 ingredients (through mushrooms) to pan; cook 8 minutes or until mushrooms are browned and tender, stirring occasionally. Add broth and 1/4 teaspoon pepper; cook 4 minutes or until liquid almost evaporates. Remove from heat; keep warm.
6. Bring 6 quarts water to a boil in each of 2 large Dutch ovens. Add 12 ravioli to each pan; cook 4 minutes or until ravioli float to the surface. Remove ravioli from water with a slotted spoon. Place ravioli on a tray, making sure they do not overlap; cover and keep warm. Return water in 1 Dutch oven to a boil. Add shaved asparagus; cook 15 seconds. Drain.
7. Place 4 ravioli on each of 6 plates; top each serving with 1/2 cup sauce and 1/4 cup asparagus. Sprinkle each serving with 4 teaspoons cheese.