Method
Put the eggs into a medium saucepan and add water to cover by 1 inch. Set the pan over high heat and bring the water to a boil. The moment it comes to a full boil, turn off the heat, cover the pot and set a timer for 10 minutes. Meanwhile, prepare a large bowl of ice water.
When the timer rings, transfer the eggs to the ice water. Once the eggs are cool enough to handle, peel them. If you are having trouble peeling them cleanly (it happens, especially if your eggs are very fresh), place them, one at a time, in a clean jelly jar with about 3 tbsp water, screw on the lid tightly, and shake the jar like mad. The shell should come off much more easily.
Cut each egg in half lengthwise, carefully remove the yolks from the whites, and reserve the whites. Put the yolks into a food processor, add the mayonnaise, the Curry Mustard (or regular mustard), the lemon juice, Guntur Sannam Hot Sauce and salt and puree until smooth. (You can instead do this in a bowl with a fork but it won't be quite as smooth.) Season to taste with a bit of more salt if needed.
Use a small spoon to fill the egg whites with the yolk mixture. Sprinkle with the chives and serve immediately.