Roasting vegetables adds a satisfying, bold flavor dimension to soup. Be sure to roast the vegetables long enough for the onions to get well done, as undercooking them will give the soup a raw flavor. Because roasting leaves a brown skin on the potatoes, the soup wont be perfectly smooth when you puree it. But dont worry: A few chunks in the soup contribute to the texture.
Preheat oven to 400°F. Place potatoes in large bowl. Snip root end off each onion and cut each half into 3 sections. Add onions to potatoes, breaking up onions with your fingers to separate.
Drizzle vegetables with oil, add thyme and toss well. Spread vegetables on baking sheet. Season with salt and pepper.
Slice top third off head of garlic and place it on a piece of foil. Put 1/2 tablespoon butter on top of garlic and drizzle 2 teaspoons water onto foil. Fold sides of foil to enclose; place on pan with vegetables. Roast vegetables 45
minutes, then remove garlic. Continue roasting vegetables until tender, about 15 minutes more.
In large saucepan, bring broth to a simmer over medium-low heat. Transfer half the roasted vegetables to food processor and add 1/2 cup hot broth. Process mixture until fairly smooth, then transfer to bowl. Repeat with remaining vegetables and a little more hot broth, squeezing garlic pulp out of husks into last batch. Stir all pureed mixture into broth in pan; keep pan over low heat.
In small saucepan, melt remaining 2 tablespoons butter over medium-low heat. Add flour and cook, stirring constantly, 1 1/2 minutes. Stir in milk and cook, stirring often, until thickened, about 3 minutes. Stir in ladleful of soup and cook 1 minute.
Add mixture back to soup. Cook over medium-low heat until heated through, stirring occasionally, about 10 minutes. Serve right away, or cool, refrigerate and reheat when needed.