Remove the fat and rind from the bacon. Cut the bacon into strips.
Heat the oil in a medium saucepan. Fry the garlic and onion together with the bacon over low heat, stirring constantly, for about 5 minutes until translucent. Add mushrooms and fry for another 5 minutes. Stir in parsley, peas and condensed milk. Mix the cornstarch with the water and add to the sauce. Thicken slightly over medium heat while stirring.
Meanwhile, cook the pasta in a large saucepan with boiling salted water for 8 minutes until al dente. Drain through a sieve.
Arrange the linguine on plates. Spread the hot sauce on top and serve garnished with Parmesan shavings.