How to Make It
Make the salsa verde: Sprinkle the minced shallot with 1/2 teaspoon salt. Add the tomato vinegar, and let stand 20 minutes.
Process the herbs, 1/2 cup olive oil, garlic, and piment d’Espelette in a blender on high speed to reach a pesto-like consistency. (Do not overblend or sauce will turn brown.) Place salsa verde in an airtight container; chill until ready to serve.
Make the chickpea fritters: Puree 6 tablespoons olive oil and garlic cloves in a blender until smooth. Pour through a fine wire-mesh strainer into a small bowl, pressing gently on solids. Discard solids.
Bring 2 1/2 cups water to a boil in a medium pot, covered, over high heat. Whisk in chickpea flour and 11/2 teaspoons salt until smooth. Fold in oil mixture with a heatproof spatula. Reduce heat to moderately low. Cook, stirring often with spatula to ensure mixture does not stick to sides or bottom of pan, 15 minutes. Remove from heat, and cool slightly. Place mixture in a food processor; process until smooth.
Place chickpea mixture in a quarter sheet pan or 9-by-13-inch pan lined with plastic wrap. Top with another layer of plastic wrap and press mixture to fill pan. Mixture should be about 1/4 inch thick. Chill until set, about 30 minutes.
Heat neutral oil in a large saucepan or small Dutch oven to 350°F.
Break chickpea mixture into roughly 1-inch squares. Fry in 3 to 4 batches, agitating gently with a mesh skimmer or large slotted spoon to ensure even frying, until crispy and slightly golden, 3 minutes. Drain on paper towels. Sprinkle with remaining 1 1/2 teaspoons salt.
Drain shallots and add to salsa verde. Season with remaining 1/4 teaspoon salt and stir to combine. Serve fritters with salsa verde.