Heat a large high sided skillet over medium heat. Add bacon, and cook until browned and crispy. Remove bacon and set aside on a cutting board. Once cool enough to handle, roughly chop into small pieces.
Add squash, onion, garlic, tarragon, and salt and pepper, and mix to coat in bacon fat. Cook, stirring occasionally, about 10 minutes or until onions are soft and translucent.
Add stock, and bring mixture to a boil. Reduce heat to maintain a simmer, and cook until squash is tender, 15-20 minutes. Liquid should reduce by half and the squash easily pierced with a fork.
Meanwhile, cook pasta in a large pot of boiling salted water, according to the directions. Reserve 1/2 cup of the cooking liquid.
Set vegetables aside to cool slightly, then carefully transfer to a high powered blender or food processor. Blend until smooth and creamy. Season with additional salt and pepper as desired.
In the same pan you cooked the vegetables, pour in the puréed sauce, 3/4 of the chopped bacon, 1/4 cup of the reserved pasta water, and cooked pasta. Heat over medium heat, until warmed throughout and sauce easily coats the noodles. If the sauce is too dry, add extra pasta water as needed.
Serve immediately topped with remaining bacon pieces, extra chopped tarragon, shaved cheese, and extra cracked pepper if desired.