Preheat the oven to 400°F. Place on a doubled piece of foil:
Drizzle with:
Wrap and seal tightly. Place on a baking sheet and roast for 1 hour.
Remove the package from the oven, carefully open, and let cool. When cool enough to handle, squeeze the garlic and shallots from their skins into a small food processor or a blender. Add and process to a puree:
With the machine running, add in a slow, steady stream, processing until smooth:
Taste and adjust the seasonings. Use immediately, or cover and refrigerate for up to 5 days.