Finely mince ½ shallot and transfer to a small bowl. Grate 1 small clove garlic on a microplane and add it to the shallot.
Add 1½ teaspoons Dijon mustard, ½ teaspoon sea salt, ¼ teaspoon freshly ground black pepper, and 3 tablespoons Balsamic vinegar. Whisk well to combine.
Add ½ cup + 1 tablespoon extra virgin olive oil a few tablespoons at a time, whisking after each addition until the dressing is emulsified. Continue adding the olive oil by the tablespoon until it's all been used and the balsamic vinaigrette is thick and creamy.
Taste for seasonings and adjust as needed to your tastes.
Video
Notes
Store the dressing in a jar with a tight-fitting lid in the refrigerator.
This homemade balsamic vinaigrette will keep well in the refrigerator for about 1 week.