In a medium bowl, whisk together the balsamic vinegar, Dijon mustard, granulated sugar, kosher salt, and black pepper until the salt dissolves. Whisk in the garlic paste.
While whisking constantly, slowly stream in the extra-virgin olive oil until the vinaigrette is smooth and emulsified, 1–2 minutes. Alternatively, combine all ingredients in a jar, seal, and shake vigorously for 30 seconds until emulsified.
Taste and adjust seasoning with a pinch more salt or sugar if needed. Let stand 10 minutes to meld flavors.
Use immediately, or refrigerate in a sealed jar for up to 1 week. Shake or whisk to re-emulsify before serving.