Over medium heat, melt butter in a large saucepan. Add onion and mushrooms, saute until tender.
Whisk in flour. When combined, slowly whisk in milk.
Lightly boil until thickened.
Add tuna, peas and spices. Reduce heat and simmer for 5 minutes.
Toast English muffins. Top muffins with a cheese slice when hot. If you want the cheese melted further, slip into a hot oven for 2-3 minutes.
Using a ladel, top the English muffins with the creamy tuna. Serve alongside a generous green salad.