Chilled Shrimp & Cucumber Salad with Sweet & Spicy Ginger Vinaigrette

1 large hot house cucumber, sliced thinly into about 48 rounds (use a mandoline here, if you like)

20 small shrimp, cooked, sliced in half lengthwise & chilled

1 large head frisee

1/4 cup mint leaves (about 16 large leaves), torn

1 large carrot, sliced into fine julienne

Vinaigrette:

3 ounces olive oil

2 ounces Ginger Syrup

2 ounces rice vinegar

1/2 teaspoon chopped mint

Pinch of togarashi or cayenne pepper

1/4 cup crushed peanuts, for garnish

Kosher salt and freshly ground black pepper