A note on shaving asparagus: while the other vegetables are best sliced thin on a mandolin, you'll have the most luck using a vegetable peeler to get thin asparagus strips. Instead of cutting off the woody ends, lay the asparagus spear down on a cutting board and hold on to the end. Starting about ½ an inch above your fingers, use the peeler to shave off a thin strip. Continue until you've gotten all the way to the bottom, then discard the woody end.
In a large bowl, combine shaved asparagus, cucumbers, radishes, garlic, and snap peas.
In a small bowl, whisk together olive oil, lemon juice, mustard, and salt. Pour over vegetables and toss to coat.
Spread vegetables out onto serving platter, then top with burrata. Gently cut open burrata so the creamy cheese oozes out, sprinkle with freshly ground black pepper and serve.