To begin, trim the ends of the green beans and remove any fibrous strings. Cut longer beans in half for even cooking. Move to blanching.
Bring a pot of salted water to a boil. Add the beans and cook for 2–3 minutes until bright green and just tender. Drain and plunge into ice water to stop cooking. Pat dry thoroughly before battering.
In a mixing bowl, combine flour, baking powder, salt, and pepper. Lightly beat the egg and add it to the dry ingredients along with cold sparkling water. Whisk gently until smooth, avoiding overmixing to maintain a light texture. Proceed to heating the oil.
In a deep pan or fryer, heat vegetable oil to 180°C. Test by dropping a little batter in; it should sizzle and float immediately. Move to coating beans.
Dip a handful of beans at a time into the batter, ensuring they are fully coated. Shake off excess batter to prevent heavy clumps. Continue with remaining beans.
Carefully lower the coated beans into the hot oil. Fry for 2–3 minutes until golden and crisp. Work in batches to avoid overcrowding and lowering the oil temperature. Move to draining.
Remove the fritters with a slotted spoon and place them on kitchen paper to drain excess oil. Sprinkle immediately with coarse sea salt for best adhesion.
Serve Peixinhos da Horta immediately with lemon wedges. Presentation tip: pile the fritters high on a platter and serve with a chilled vinho verde for an authentic Portuguese experience.