How to Make It
Make the fritters In a medium bowl, whisk the flour with the cornmeal, baking powder, baking soda, cheese, 1/2 teaspoon of salt and 3/4 teaspoon of pepper. In another medium bowl, whisk the milk with the buttermilk, egg, chives, anchovies and anchovy oil. Stir the wet ingredients into the dry ingredients until just combined. Cover and refrigerate the batter for 1 hour.
Meanwhile, make the salad In a blender, puree the anchovies with the egg yolk, shallot, garlic, mustard, vinegar, lemon juice, piment d’Espelette and 1 teaspoon of salt until smooth. With the machine on, drizzle in the 1 cup of olive oil until incorporated. Transfer the dressing to a small bowl and stir in the finely grated Parmesan.
In a medium saucepan, heat 2 inches of canola oil to 360°. Drop 8 rounded tablespoonfuls of batter into the oil and fry, turning once, until the fritters are golden brown and crisp, 1 to 2 minutes. Using a slotted spoon, transfer to a paper towel–lined plate to drain. Repeat with the remaining batter.
Arrange the lettuce and anchovy fritters on 6 plates or a large platter. Drizzle the salad with the dressing. Garnish with Parmesan shavings and a drizzle of olive oil; serve immediately.