Beat the eggs in a medium bowl and add the parmesan. Season with 1 TSP salt and lots of freshly cracked black pepper. Set aside for now.

Cook the pasta according to package directions, and be sure to reserve 1 cup of the starchy cooking water before you drain it (this is really important). 

In a large skillet, cook the bacon over med-high heat until nice and crispy. Transfer it to a paper towel-lined plate and leave 1 TBSP of the drippings behind in the pan (drain the rest). Reduce the heat to medium and add the onion. Cook until nice and tender; 6 to 8 minutes, stirring occasionally. Add the tomato paste, garlic, brown sugar, balsamic vinegar, and the bacon. Stir to combine and cook for about a minute so the garlic isn’t raw. Turn off the heat.

Add the hot pasta into the pan with the bacon jam mixture and, using tongs, toss to mix. Add some of the hot, bacony pasta mix to the bowl with the eggs (to temper them, increasing their temerpature). Then pour the egg/parm mixture into the pasta. Toss again (toss toss toss) to help a creamy sauce develop, and add in some of the reserved pasta water to help with that, if needed. 

Taste, season with more salt/pepper as needed, and serve with some torn burrata pieces and a sprinkle of crushed chili flakes.