Wash the cucumber and trim the ends. Slice very thin, about 1/8 inch thick.
Toss slices with 1 tsp salt in a colander. Rest 20 to 30 minutes until water pools below.
Rinse briefly if very salty, then pat completely dry with a clean kitchen towel.
Make the spread
Whisk hung curd in a bowl until smooth and fluffy, about 30 seconds.
Fold in mint, cilantro, green chili (if using), lemon juice, salt, pepper, and chaat masala (if using). Taste and adjust.
Assemble the sandwiches
Spread a thin layer of butter on one side of each bread slice if using.
Spread herbed hung curd on half of the slices. Top with a single layer of cucumber.
Close with remaining bread, spread-side down. Press gently.
Trim crusts if desired. Cut into fingers or small triangles.
Serve
Arrange on a platter and garnish with mint. Serve within 1 to 2 hours for the best texture.
Notes
Line a strainer with cheesecloth and drain plain yogurt 2 to 4 hours for hung curd. Greek yogurt works in a pinch.Make the spread up to 1 day ahead. Drain cucumber and assemble close to serving.Vegan swap: blend soaked cashews with unsweetened plant yogurt, lemon, and the same herbs until thick. Chill before spreading.Wrapped tightly, assembled sandwiches keep up to 8 hours in the fridge. Texture is best the day they are made.