Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve 1 cup of the starchy pasta water.
Render the bacon: Slice the bacon into 1/2-inch pieces. Add to a cold large skillet, then turn heat to medium. Cook, stirring occasionally, until deeply crispy, about 6-8 minutes. Transfer bacon to a paper towel-lined plate, leaving about 2 tablespoons of rendered fat in the pan.
Start the sauce base: Reduce heat to low. Add the softened cream cheese to the bacon fat in the pan. Stir constantly with a wooden spoon or silicone spatula until fully melted and smooth, about 1 to 2 minutes. It will look tight at first; keep going.
Temper with pasta water: Ladle in 1/2 cup of the reserved pasta water. Whisk vigorously until the sauce is smooth, pourable, and emulsified — it should look like a rich, creamy gravy. Add another splash if needed.
Add the cheese: Remove the pan from the heat. Stir in the grated Parmesan and a generous crack of black pepper until fully melted and smooth. Taste before adding salt — bacon and Parmesan are already salty.
Combine: Drain the pasta (reserving extra water) and add it directly to the sauce. Toss for 30-60 seconds over low heat until every piece is coated. If the sauce is too thick, add a splash of the reserved pasta water.
Finish: Fold in most of the crispy bacon, reserving a few pieces for the top. Serve immediately in warm bowls. Top with remaining bacon, a tangle of fresh chives, and a final pinch of flaky salt.