Mushroom Welsh rarebit toastie with a fried egg

Name: Mushroom Welsh rarebit toastie with a fried egg
Prep time: 30 min
Total time: 30 min
Cuisine: British
Ingredients: Knob of butter for frying; 300g mixed mushrooms, roughly chopped or sliced; 1 tbsp chopped fresh tarragon; 4 white crusty bread slices; 1 tbsp vegetable oil for frying; 2 large free-range eggs; 80g extra-mature cheddar, grated; 25g mozzarella, grated; 2 tbsp cornflour; 80ml stout; 1 tbsp English mustard; A few dashes Henderson’s Relish (or vegetarian Worcester sauce, such as Biona); 2 large free-range egg yolks