Preheat oven to 350°F. Bring milk, butter, and salt to a simmer in a medium saucepan. Reduce heat, gradually whisk in cornmeal, and simmer, stirring, until thickened, about 2 minutes.
Remove from heat; whisk in pumpkin purée.
Whisk egg yolks, chives, thyme, cinnamon, cayenne, ginger, and nutmeg in a large bowl.
Whisk in cornmeal mixture.
Using an electric mixer, beat egg whites in a medium bowl until soft peaks form.
Whisk 1/4 of whites into batter, then gently fold in remaining whites. Scrape batter into a 9x5" loaf pan.
Bake until spoon bread is set and begins to pull away from sides of pan, 30–40 minutes.