In a medium bowl, whisk together vinegar, lemon juice, mustard and shallot until combined. Add olive oil in a slow stream, whisking constantly until emulsified. Whisk in salt and several grinds of pepper. Check for seasoning and add more salt and/or pepper to taste. Serve or refrigerate for up to 2 weeks.
Video
Notes
If olive oil solidifies in refrigerator; remove 15-30 minutes before serving to warm and liquify. Whisk vinaigrette to combine before serving.