Step 1

Adjust oven rack to middle position and heat oven to 375 degrees F/191 degrees C. Combine olive oil, vegetable oil, salt, and pepper in small saucepan. Place garlic heads, cut side down, in saucepan; cover and transfer to oven. Cook until cut side of garlic is deep golden brown and cloves are soft and easily pierced with paring knife, about 45 minutes.

Step 2

Using tongs, transfer garlic heads to plate and set aside until cool enough to handle; reserve oil in saucepan. Squeeze root end of each head until cloves slip out of their skins; discard skins. Transfer roasted garlic cloves to blender along with water, vinegar, miso, and tahini. Process on high speed until well combined, about 30 seconds. Scrape down sides of blender jar with rubber spatula. With blender running on low speed, slowly drizzle in reserved oil until dressing is emulsified and thickened, about 45 seconds. Season with salt and pepper to taste. Transfer dressing to airtight container and refrigerate until ready to use. (Dressing can be refrigerated for up to 1 week.)