MAKE THE CHICKPEA FRITTERS: Spray a non-stick quarter sheet pan with non-stick vegetable spray.
In a medium bowl, whisk the chickpea flour, salt, pepper and nutmeg until well combined.
Meanwhile, in a medium-sized high-sided skillet, bring 3 cups of cold water to a gentle simmer.
Add the chickpea flour mixture to the water in a slow, steady stream, whisking constantly to avoid lumps.
Continue to mix constantly, switching to a rubber spatula, if necessary, until the batter thickens, for 1 to 2 minutes.
Dump the batter onto the prepared sheet pan, and, using a small offset spatula, spread it evenly into the sheet pan. It should be approximately ¼-inch in thickness.
Refrigerate until set, about an hour.
MAKE THE RICOTTA CREAM: In a medium-sized bowl, whip the ricotta, pecorino, parsley and pepper until creamy
Season with salt, to taste; refrigerate until ready to assemble sandwiches.
Cut the chickpea sheet into 12 equal pieces.
Fill a large, high-sided frying pan with a ¼-inch of vegetable oil and heat over medium-high heat until it shimmers.
Fry the chickpea fritters in batches until lightly golden brown, for 2 to 3 minutes per side.
Transfer to a paper towel-lined plate to absorb any excess oil.
To ASSEMBLE the sandwiches, place two chickpea fritters on the bottom half of the brioche bun. Dollop with a generous scoop of ricotta cream. Top with the brioche lid and serve immediately.