Make the lemon yogurt: In a small bowl whisk the Greek yogurt with the fresh lemon juice and a pinch of salt and black pepper until smooth. Taste and adjust acidity — the lemon brightens the yogurt and will cut the richness of the egg, so keep it lively but not sour. Refrigerate while you prepare the batter so it stays cool.

Prepare the pea purée (if not already done): If using frozen peas, blanch 1 1/3 cups in boiling water for 60–90 seconds then plunge into ice water to preserve color. Drain and pulse briefly in a food processor or mash coarsely with a fork — you want a slightly textured purée so the pancakes have pleasant little pea bursts. A completely liquid purée will thin the batter too much.

Whisk the batter: In a medium bowl combine the chickpea flour, a generous 1 tsp salt, 1/2 tsp black pepper, and the optional 1/2 tsp ground cumin if using. Add the pea purée, chopped mint, and any optional grated garlic. Add about 3/4 cup cold water gradually while whisking to make a pourable batter the consistency of slightly thick cream (roughly 3 tbsp water per person as you specified). Chickpea flour needs time to hydrate; whisking and letting it rest creates a tender interior while a slightly thick batter helps the pancakes hold together and crisp on the exterior.

Rest the batter 8–12 minutes: Cover the bowl and let it sit at room temperature. Resting lets the chickpea flour absorb liquid and removes any raw 'beany' edge, yielding a silkier mouthfeel and better binding so the cakes don't fall apart when flipping.

Heat the pan: Warm a nonstick skillet or well-seasoned 10–11 inch cast-iron pan over medium heat until shimmering but not smoking. Add 1 tsp olive oil per person (you can add 1–2 tsp to the pan to start and add more between batches). A properly preheated pan creates immediate contact-searing to form a golden-brown crust that contrasts the tender interior.

Cook a test pancake: Spoon about 3 tablespoons of batter per pancake (or ~1/4 cup if you prefer large cakes) into the hot pan, spreading lightly into a 3–4 inch round. Cook 2–3 minutes on the first side until the edges look set and the underside is deeply golden. Flip and cook 1–2 minutes more. Testing ensures your pan temperature and batter thickness are correct; if the pancake browns too quickly or remains raw inside, adjust the heat and batter thickness.

Cook remaining pancakes in batches: Keep the heat between medium and medium-low: too hot will burn the outside before the inside cooks, too low will prevent browning. Add a little more oil between batches if the pan becomes dry. Transfer cooked pancakes to a warm plate and loosely cover with foil to stay warm while you finish the batch.

Poach the eggs: Bring a wide, shallow saucepan of water to a gentle simmer (not a rolling boil) and add a teaspoon of white wine vinegar per liter of water (optional — it helps the whites coagulate). Crack each egg into a small cup and lower it into the water, poaching 3–3 1/2 minutes for a runny yolk or 4 minutes for slightly set. A gentle simmer and fresh eggs produce a neat white and tender yolk; agitation or high heat will break the egg apart.

Finish and plate: Spread about 2 tablespoons of lemon yogurt on each plate, top with 2–3 warm chickpea-pea pancakes, place a poached egg on top, and season each egg with flaky salt and a grind of black pepper. Scatter a few extra mint leaves and a light drizzle of olive oil over the assembled dish for gloss and aroma. The lemon yogurt provides acidity, the pancakes deliver texture and savory depth, and the runny yolk acts like a rich sauce that ties everything together.

Serve immediately: These are best eaten right away while the pancakes are crisp at the edges and the poached egg is warm and runny. Provide extra lemon wedges and hot sauce on the side if desired.