どうしても書くとしたらこうかな

public partial class Parent : Form
{
public Parent() {
InitializeComponent();
}

private void button1_Click(object sender, EventArgs e) {
new Child(this.Click).ShowDialog();
}

private void Click(object sender, EventArgs e) {
MessageBox.Show("またクリックしたの？");
}
}

public partial class Child : Form
{
private EventHandler eventHandler;

public Child(EventHandler eventHandler) {
InitializeComponent();

this.eventHandler = eventHandler;
}

private void button1_Click(object sender, EventArgs e) {
this.eventHandler(this, EventArgs.Empty);
}
}