In a small bowl, combine the shallot, white wine vinegar, Dijon mustard, kosher salt, and black pepper; let sit 5–10 minutes to lightly pickle the shallot.
Whisk while slowly drizzling in the extra-virgin olive oil until the vinaigrette is glossy and slightly thickened, 1–2 minutes.
Taste and adjust seasoning and acidity as needed.
Use immediately to dress greens, vegetables, or grains, or refrigerate in a sealed jar up to 1 week. Shake to re-emulsify before using.