Make the vinaigrette: Add the garlic, salt, pepper, lemon juice, olive oil, champagne vinegar, honey, and Dijon mustard to a blender or bowl. Blend or whisk until completely combined and emulsified. Set aside.
Assemble the salad: Add the shaved Brussels sprouts to a large bowl. Season with a pinch of kosher salt and gently massage and toss them with your hands. This helps soften and season them.
Pour half of the vinaigrette over the Brussels sprouts and toss well, making sure every piece is coated. Let sit for about 5 minutes so the sprouts absorb the dressing and soften even more.
Add most of the pomegranate seeds, Manchego shavings, and dates (carefully separating clumps if necessary), saving a third of each to use later. Add all of the pistachios and the parsley, and toss gently to combine.
Taste and add more vinaigrette if needed. Finish with the reserved Manchego, dates, and pomegranate over the top and serve.