Bring water and salt to a boil in a large stockpot over high heat. Add pasta to boiling water, and reduce heat to medium high. Cook pasta until almost al dente, stirring occasionally, about 8 to 9 minutes.

Meanwhile, cook bacon in a large nonstick skillet over medium heat, stirring constantly, until fat is rendered and edges of bacon are crisp but centers are still pliable, about 5 minutes. Transfer bacon to a paper towel using a slotted spoon. Reserve 1 tablespoon bacon drippings in skillet; pour out remaining oil and reserve for another use.

Whisk together egg yolks, whole egg, and grated Parmesan in a large bowl until well combined; set aside. 

Once pasta is almost al dente, use a heat-proof 2-cup liquid measuring cup or ladle to reserve 2 cups pasta water, then drain pasta; set aside. Add garlic to skillet and cook over medium, stirring constantly, until fragrant, about 1 minute. Add bacon back to skillet with pasta; toss to coat. Pour pasta mixture into bowl with egg mixture; toss to coat. Add mixture back to skillet with 1/2 cup pasta water, and cook, stirring constantly, over medium-low until starting to thicken, about 3 minutes. Add up to 1/2 cup more pasta water if needed to create a thick, but glossy sauce, tossing pasta constantly in skillet to prevent eggs from curdling. Transfer pasta back to large bowl; top with freshly grated parmesan and cracked black pepper and toss to coat. Serve with more cheese and pepper, if desired.