Typescript object declaration where each prop has its own generic

Question

I am trying to create a more dynamic object typing. Right now I have the following:

interface MyGeneric<T> {
  value: T
}

interface MyObject {
  [name: string]: MyGeneric<any>;
}

But I want to abstract it to look more like this:

interface MyGeneric<T> {
  value: T
}

interface MyObject {
  [name: string]<T>: MyGeneric<T>;
}

This syntax does not work, but what I want would allow each prop on the object to have its own generic type.

Any advice on what this might look like?