Cook bacon in large skillet over medium heat until crisp, about 8 minutes. Using slotted spoon, transfer bacon to paper towel to drain. Pour off all but 2 tablespoons fat from skillet if necessary. Add mushrooms and saute over medium heat about 3 minutes. Add green peas and saute for 2 more minutes. Add 1 tablespoon olive oil and add leeks and sauté over about 6 minutes. Set aside.
Meanwhile, cook pasta in large pot of boiling salted water until just tender but still firm to bite, stirring occasionally. Drain pasta, reserving 1/2 cup pasta cooking liquid.
Whisk eggs and 1/2 cup Parmesan in medium bowl to blend; gradually whisk in 1/4 cup pasta cooking liquid. Add pasta to leeks and mushroom mixture in skillet and stir to heat. Remove skillet from heat. Pour egg mixture over pasta and stir until sauce is just creamy and eggs are no longer raw, about 2 minutes. (Return skillet to very low heat if egg mixture is runny; do not overcook or eggs will curdle.) Add some of remaining 1/4 cup pasta cooking liquid to pasta if needed to moisten. Stir in bacon and parsley. Serve pasta, passing additional cheese separately.