How to add a method to a prototype of a generic class in typescript

Interfaces do not exist at runtime, they are erased during compilation, so setting the value of a function on an interface is not possible. What you are probably looking for is adding the function to Promise. You can do this similarly:

declare global {
  interface Promise<T> {
      handle(): Promise<T>;
  }
}

Promise.prototype.handle = function<T>(this: Promise<T>): Promise<T> {
  return this;
}