Peel shallots, and toss with 1 Tbsp. olive oil in a large bowl. Arrange shallots on an aluminum foil-lined baking sheet.
Bake at 400 for 25 minutes or until shallots are very tender, turning once after 15 minutes.
Remove from oven, and let cool 10 minutes.
Pulse roasted shallots, white wine vinegar, and next 4 ingredients in a food processor 3 to 5 times or until thoroughly blended. With processor running, slowly pour 1/3 cup olive oil through food chute in a slow, steady stream, processing 15 to 20 seconds or until mixture is blended and smooth.
Serve immediately. Store vinaigrette in an airtight container in refrigerator for up to 5 days.
Let stand at room temperature for 10 minutes, and whisk just before serving.
