Use a mandoline to slice carrots and ginger into very thin slices. Use a sharp knife to cut slices lengthwise into fine shreds.
In a small skillet over medium-high heat, heat ¼-inch canola oil. Add a handful of the vegetables and fry until golden brown and crisp, about 1 minute. Remove with a slotted spoon and transfer to a paper towel-lined plate. Sprinkle lightly with salt. Repeat with remaining vegetables.
Pan-fried Crab Ravioli
In a bowl, combine ricotta, crab meat, 1 egg, parsley, lemon juice, ½ teaspoon salt and black pepper to taste.
Beat remaining egg in a small bowl. Place 1 wrapper on a clean work surface, brush with beaten egg and spoon 1 Tablespoon of filling in the center of each wrapper. Top with a second wrapper. Use your fingers to seal edges and trim with a fluted cutter, if desired. Repeat filling, sealing and cutting until all of the filling has been used.
Melt 1 Tablespoon butter with 1 Tablespoon olive oil in a large skillet over medium heat. Add ravioli in a single layer and cook until golden and crisp, about 3 minutes per side. Transfer to a platter. Wipe out skillet, heat another Tablespoon of butter and olive oil in the skillet until melted, and repeat pan-frying ravioli until all of the ravioli have been cooked.
To serve, drizzle with pomegranate molasses and sprinkle with frizzled carrots and ginger. Serve warm.