In a 4- to 5-quart pan, frequently stir onion, garlic, pumpkin pie spice, cayenne, and 1/4 cup broth over high heat until pan is dry, about 3 minutes.
In a blender or food processor, smoothly purée onion mixture, adding a little more broth if needed to facilitate the process.
Return purée to pan; add remaining broth, pumpkin, and honey.
Smoothly mix milk with cornstarch and stir into soup. Stirring, bring to a boil over high heat. Add lemon juice and salt to taste.
Ladle soup into shallow bowls. Stir sour cream to soften, then drizzle a small amount into each bowl.