For the most delicious results, use the best olive oil–packed tuna you can find. Slideshow: Gluten-Free Recipes
In a medium bowl, whisk the buckwheat flour with the eggs and half of the milk until lump-free. Add the remaining milk and whisk until smooth. Refrigerate the batter for 20 minutes.
Meanwhile, in another medium bowl, mix the tuna with the apple, shallot, mayonnaise and lemon juice.
In a small bowl, whisk the mustard with the vinegar and salt. Gradually whisk in the 1/4 cup of olive oil, then season the vinaigrette with salt.
Line a plate with wax paper. Heat an 8-inch nonstick skillet and lightly brush with olive oil. Add 1/4 cup of the batter to the skillet and swirl to coat the pan. Cook over moderate heat until the edges begin to pull away from the pan, 30 seconds to 1 minute. Flip the crêpe and cook 30 seconds to 1 minute longer. Transfer the crêpe to the prepared plate and repeat with the remaining batter.
Divide the tuna salad between the crêpes and top with the arugula. Drizzle with the vinaigrette and serve.