Green Garlic Panisse

Line a half sheet pan (13 by 18 by 1-inch pan) with oiled parchment paper.
Split the garlic lengthwise and rinse carefully to remove any dirt. Dry the garlic on a towel, then slice it as thinly as possible. Melt the butter with the olive oil, add the garlic, cover with a cartouche, and cook over low heat until translucent. Transfer to a large pot and add the milk and salt. Increase the heat to medium-high and slowly add the chickpea flour while whisking constantly to avoid lumps. Cook over high heat until the mixture begins pulling away from the sides of the pan and the starchy flavor has cooked out. Pour the dough onto the prepared pan and spread evenly. Zest the lemon over the entire surface. Place plastic wrap directly on top of the panisse to prevent a skin from forming. Refrigerate for about 1 hour, until completely set. Cut into desired shapes.
Heat the grapeseed oil to 350°F (175°C) and fry the panisse pieces in small batches for about 30 seconds, until golden brown and crispy. Drain on paper towels, arrange on a platter, and serve immediately.