Preheat oven to 350°. In a large bowl, whisk vinegar, oils, and a pinch of fine salt.
Use a mandoline or sharp knife to slice carrots lengthwise into thin ribbons. Place in a bowl of ice water until they start to curl, about 7 minutes; then drain well, pat dry with a kitchen towel, and add to vinaigrette.
Right before serving, add lettuces to carrots, along with half the pistachios, half the dill, and a pinch of fine salt.
With a serving spoon, dollop 1/4 to 1/3 cup carrot borani onto each of 6 to 8 salad plates (or 1 to 2 cups on a large platter). Use back of spoon to spread borani into thick beds. Loosely mound salad on borani, then top with remaining pistachios, dill, and a pinch of flaky sea salt.
Serves 6 to 8 as a first course or side (14 cups)