Instantiate HashMap, ?> with given Class variables?

I got a Java function with the following signature:

public void foo(Class<? extends Base1> varClass1, Class<? extends Base2> varClass2) {
  // ...
}

In this function, I need to instantiate a HashMap with type:

Map<varClass1, varClass2> map = new HashMap<>();

Of course, this doesn't compile, but I can't think of any other way to make it compile. I was surprised that even the following doesn't work:

Map<Class<? extends Base1>, Class<? extends Base2> map = new HashMap<>();

Of course, I can do:

Map<Base1, Base2> map = new HashMap<>();

But by that I loose any additional fields introduced in the sub-classes. In reality, the use-case is more complex than HashMap. I instantiate a generic class and need to work with all fields of the specified classes, so something like:

GenericClass<varClass1, varClass2> clazz =
    new GenericClass<>(varClass1.cast(var1), varClass2.cast(var2));