Prepare pasta according to package directions. Add frozen peas for the last 5 minutes of cooking. Drain, reserving the cooking water. Set aside.
Cook bacon according to package directions to crisp. Remove bacon and place on a paper towel-covered plate to drain. Allow bacon to cool enough to handle. Break bacon into bite-size pieces. Set aside.
In a large sauté pan over medium heat, melt 1 tablespoon butter.
Add chicken, cooking through completely, about 5 to 6 minutes for each side. Remove chicken from skillet. Slice into strips. Set aside and keep warm.
Place a small saucepan over medium heat. Add 2 tablespoons butter.
When butter has melted and is hot, add garlic. Cook 1 minute.
Whisk in the 1/4 cup Parmesan cheese and the flour.
Slowly whisk in the evaporated milk. Bring to a boil. Reduce heat. Boil gently, uncovered, until sauce has thickened. Remove from heat.
Stir in bacon pieces.
Place prepared spaghetti mixture in a large bowl.
Pour sauce and 1/2 cup of the reserved cooking water over top. Toss gently to combine. Thin to desired consistency with more of the reserved cooking water, if necessary.
Taste. Add salt and pepper, to taste, if needed.
Top with several slices of chicken.
Sprinkle with snipped parsley and additional grated Parmesan cheese.
Serve hot.