Step 1Separate the leaves from the Brussels sprouts. To remove the leaves quickly and easily, core the sprouts at their base using a paring or tourne knife, then lightly press the cored sprouts to loosen the leaves.
Step 2In a medium, heavy-bottomed pot, add enough vegetable oil to come up the sides of the pot by about 3 inches. Heat the oil until a thermometer inserted reaches 360 degrees.
Step 3While the oil is heating, make the vinaigrette: In a medium bowl, whisk together the olive oil and vinegar. Season to taste with salt and pepper.
Step 4Deep-fry the Brussels sprout leaves, a small handful at a time, just until the leaves begin to crisp around the edges, 15 to 30 seconds. Be careful, because the oil may splatter a bit as the leaves are added. Remove the leaves immediately and drain on a paper-towel lined rack, pressing the leaves with paper towels to remove excess oil. Continue frying the leaves, in small batches, until all of them are cooked.
Step 5To assemble the dish, place the fried leaves in a large bowl, add one-half of the vinaigrette, along with the chile flakes, capers, almonds and parsley. Gently toss, then taste and adjust the flavorings and seasonings as desired. Serve immediately.