To hard-boil eggs: Place eggs in a single layer in a saucepan; cover with water. Bring to a simmer over medium-high heat. Reduce heat to low and cook at the barest simmer for 10 minutes. Remove from heat, pour out hot water and cover the eggs with ice-cold water. Let stand until cool enough to handle before peeling.
Halve eggs lengthwise with a sharp knife.
Gently remove the yolks.
Place 16 yolk halves in a food processor (discard the remaining 8 yolk halves or save for another recipe).
Add cottage cheese, mayonnaise, chives (or scallion greens), relish, mustard and salt; process until smooth.
Spoon about 2 teaspoons yolk mixture into each egg white half.