Cast Generic<Derived> to Generic<Base> [duplicate]

I have a base WPF UserControl that handles some common functionality for derived UserControls. In the code-behind of any derived UserControl I call an event

private void SomeClick(object sender, RoutedEventArgs e) {
    HandleClick(sender);
    MyDataGrid.Items.Refresh();
}

In my base UserControl I do

public class BaseUserControl : UserControl {
   protected void HandleClick(object sender) {
       var vm = (BaseViewModel<Part>)DataContext;
       ...
   }
}

This throws an InvalidCastException since DataContext is of type BaseViewModel but of a derived type like BaseViewModel<Wire> or BaseViewModel<Connector>.

How can I cast that?

You cannot cast a Generic<Derived> to a Generic<Base>.

Just imagine if you could. You have a List<Wolf> and cast it to a List<Animal>. Now you could .Add() a Sheep to your List<Animal>. But wait... now your List<Wolf> contains a Sheep. What a mess.

This would only work out if you could make sure that the thing you cast to is read-only in all possible forms. This is was co- and contravariance is all about. It only works for interfaces though.