Place all of the ingredients, except the oils, in a blender and process on high speed. With the machine running, gradually add the olive and walnut oils until the vinaigrette is emulsified, about 1 minute. Refrigerate until ready to serve. (The vinaigrette can be prepared up to 1 week in advance, covered and refrigerated.)
Note: To toast walnuts, place the walnuts in a single layer on a baking sheet. Bake in a preheated 350 degrees F. oven, stirring occasionally, until toasted, 8 to 12 minutes. Cool completely.