Place the bacon in a large, deep skillet and place over medium heat. Cook the bacon until very crisp, about 7 minutes. Remove the bacon from the skillet and place in a bowl lined with paper towel. Set aside.
Add the chicken to the skillet with a healthy pinch of salt. Sauté until the chicken is cooked through, about 5-7 minutes. Remove the chicken from the skillet and transfer to a plate. Set aside.
Next, add the onion to the skillet with another pinch of salt and sauté until softened. About 5 minutes. Stir in the garlic and sauté for 5 minutes more. Remove the onion and garlic from skillet and transfer to the same plate as the chicken. Set aside.
Place a large pot of water on the stove and bring to a boil. Add a large pinch of salt to the water and add the pasta. Cook according to the package directions or until al dente.
While waiting for the water to boil/cooking the pasta, make the sauce. Add the wine to the hot skillet you sautéed the meat and onions in and deglaze the pan. Melt the butter into the wine and whisk in the flour to form a roux. Whisk the roux until it turns a light caramel color and gives off a nutty aroma. Start pouring in the milk slowly, whisking constantly. Bring the mixture to a gentle boil and whisk in the salt, cheese and mustard. Finally, add the pumpkin and whisk to combine. By now, your pasta should be ready.
Using tongs, transfer your pasta from the water to the skillet with the sauce. Add the reserved chicken, bacon, onion and garlic to the skillet and toss to combine. If the sauce is too thick, add some pasta water to the skillet. Sprinkle the pasta with the fresh tarragon and remove from the heat.
Divide the pasta amongst 4-6 bowls and garnish with additional cheese and fresh tarragon. Serve immediately.