Make the batter: In a medium bowl whisk 2/3 cup (90 g) chickpea flour with a pinch of sea salt and a generous crack of black pepper to season the flour evenly. Slowly add 2/3 cup (160 ml) water while whisking to a smooth, lump-free batter. The slow addition and whisking hydrate the flour uniformly and avoid lumps; chickpea flour thickens as it rests so aim for a pourable, slightly thick cream consistency (like heavy cream).

Rest the batter 10 minutes at room temperature. Resting lets the flour fully hydrate (improves texture) and lets air bubbles relax so the pancake cooks evenly without pinholes. While it rests, finely chop the dill and zest the lemon.

Season and adjust: After resting, taste a ½-tsp of batter (pantry-safe) and correct salt and pepper; add more water a tablespoon at a time if the batter feels too thick—after a short rest chickpea batters can stiffen. Stir in 1 tsp of the chopped dill to distribute herb flavor into the pancake.

Heat the pan: Heat a nonstick or well-seasoned 8–10-inch skillet over medium heat until hot but not smoking (about 1–2 minutes). Add 1 tsp (≈5 ml) olive oil and tilt the pan to coat. Heating the pan first and then adding oil prevents the oil from burning and ensures an even, quick set when the batter hits the pan—this produces a crisp, golden exterior.

Cook the pancake(s): Pour half the batter into the pan, swirling to form a roughly 5–6 inch pancake about ¼–⅓ inch thick. Cook undisturbed for 2–3 minutes until the edges set and the underside is deeply golden (use a spatula to peek). The high initial heat quickly sets the surface creating a lacy, crisp edge while the interior stays tender. Flip gently and cook 1–2 minutes more until golden and cooked through. Transfer to a warm plate and repeat with another 1 tsp oil and the remaining batter to make a second pancake.

Poach the eggs while the second pancake cooks: Bring a medium saucepan of water to a gentle simmer (not a rolling boil) and add 1 tsp white vinegar if using—vinegar helps the egg white coagulate quickly and makes a neater poach. Crack each egg into a small ramekin, create a gentle whirlpool in the simmering water with a spoon, and slide eggs in one at a time. Poach 3 minutes for a runny yolk or 3½–4 minutes for slightly more set yolks. Gentle simmering (not boiling) prevents the eggs from shredding and yields a silky exterior.

Rest and dress the arugula: Toss the baby arugula with a small pinch of salt, a crack of black pepper, the remaining tsp of chopped dill, and a light drizzle (about ¼ tsp) of olive oil—this wakes the greens and balances the chickpea pancake’s nuttiness while keeping the salad delicate. Tossing just before plating prevents wilting.

Plate: Place one warm chickpea pancake on each plate. Top with a small mound of dressed arugula, peel and place a gently poached egg on top. Finish with the remaining lemon zest, a light drizzle of olive oil, an extra pinch of flaky sea salt and more cracked pepper. The contrast of warm pancake, cool peppery arugula and hot runny yolk creates layers of texture and temperature that make the dish sing.

Serve immediately: Break the yolk so it runs into the pancake and greens, and serve—this dish is best enjoyed while the pancake is crisp and the egg is warm.