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Lay each garlic head root side down. Carefully halve each garlic bulb horizontally, revealing the garlic cloves. Lay each garlic head, cut side up, on a small piece of aluminum foil. Drizzle tops with about 1 tablespoon of extra-virgin olive oil and fold up sides of foil, completely enclosing garlic. Repeat with remaining garlic.
Place garlic bundles on baking sheet and bake until cloves are soft, about 1 hour.
Remove garlic from oven and let cool about 10 minutes still sealed.
Carefully squeeze the soft garlic out of the skins into the bowl of a medium sized food processor. Puree the garlic until smooth, adding a little olive oil if necessary.
Leave about 5 tablespoons of the garlic puree in the food processor and store the remaining amount in an airtight container in the refrigerator for up to 1 week.
To the food processor, add the mustard, vinegar, remaining olive oil, and water and puree until smooth and emulsified. Season with salt and pepper.