Place the six chicken-breast halves in a 4- to 5-quart slow cooker. Arrange them in a mostly even layer so the sauce can cover the chicken as it cooks.

Melt the cubed butter and stir in the Italian salad-dressing seasoning mix. Pour the seasoned butter over the chicken, distributing it as evenly as possible.

In a separate bowl, mix the undiluted condensed golden mushroom soup with the dry white wine until combined. Pour this mixture over the chicken.

Cover and cook on LOW for about 4 to 5 hours, beginning to check around the 4-hour mark. Continue as needed, up to about 6 hours depending on chicken size and slow-cooker performance, until the chicken reaches 165°F internally.

During the final 20 to 30 minutes, add the softened cream cheese and stir it into the hot sauce. Alternatively, remove the cooked chicken, stir the cream cheese into the hot sauce until smooth, and return the chicken to the slow cooker.

Cook the 12 ounces of angel hair pasta separately according to the package directions just before serving. Drain promptly so the delicate strands do not become soft or gummy.

Serve the chicken and plenty of creamy sauce over the hot angel hair pasta. Spoon extra sauce over each portion so the pasta is coated from the first bite.