Add the roasted beets to the food processor and puree. There should be 1/2 cup of puree.  Add the 2 eggs plus the egg yolk and process until smooth.  Add the salt and 2 cups of flour and process just until the dough comes together.  Turn out onto a very floured board and knead for 5 to 10 minutes, until the dough is smooth and elastic.  Cover with a bowl and let it rest for 1 to 2 hours.  

Cut the dough into 8 pieces and knead in a bit more flour if the dough is too sticky.  Follow your pasta machine manufacturers directions and make sheets of pasta.  Make pasta using the fettuccine attachment and make small piles on a floured rimmed baking sheet or use a pasta drying rack.  Repeat with all remaining dough.

Bring a large pot of salted water to a boil.  Meanwhile, heat a large skillet (big enough to hold the cooked pasta)  over high heat and add the bacon, fry until crisp and browned, drain on a paper towel lined plate and set aside.  Turn the heat down to medium.  

In a medium bowl add the eggs and Parmesan cheese and whisk to combine.  Season with salt and pepper and set aside.

Add the pasta to the boiling water and stir once.  Cook for 2-3 minutes.  

Add the garlic and peas to the skillet and heat through.  When the pasta is cooked, transfer from the water to the skillet using tongs or a spider strainer, do not drain in a colander.  Toss the pasta in the bacon fat, peas and garlic.  Slowly whisk 1 cup of the cooking liquid into the egg and Parmesan mixture and add to the pasta and toss to coat.  The hot pasta will cook the egg and make a creamy sauce.  Serve immediately in warmed bowls.