In a medium bowl, whisk together the champagne vinegar, Dijon mustard, and kosher salt until the salt dissolves.
Stir in the minced shallot and let sit 5 minutes to gently mellow its bite.
While whisking constantly, slowly stream in the olive oil until the vinaigrette is slightly thickened and glossy, 1–2 minutes.
Season with the black pepper and adjust salt to taste. Use immediately or refrigerate in a sealed jar for up to 1 week; whisk or shake to re-emulsify before serving.