1/4 cup plus 1 tablespoon extra-virgin olive oil, plus more for brushing
1 pint yellow cherry tomatoes, halved
1 tablespoon balsamic vinegar
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 a small food processor, pulse the garlic with the cashews until finely chopped. Add the basil, chives, lemon juice and 1/4 cup of olive oil; season with salt and puree until smooth.
In a medium bowl, toss the tomatoes with the vinegar and 1 tablespoon of olive oil; season 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.
Slather each crêpe with 1 tablespoon of the pesto and fold into quarters. Serve on a platter with the cherry tomatoes on top.