Welsh rarebit is a popular British comfort food. This sandwich is made with hot, smooth cheese sauce, a bite of tomato, and crispy English muffin. Kids will be just wild about this one too. Serve it hot and eat it right away so the rarebit stays warm and soft.
In a medium saucepan, whisk the egg yolks. Then add the milk and stir the liquid gently over low heat for 3 to 4 minutes, gradually raising the heat to medium low.
Add a large handful of the cheese to the liquid and stir. Continue adding and stirring in this manner until all the cheese is melted (it's fine if the previous batch is still somewhat lumpy before adding the next). Continue to stir nonstop, keeping a close eye on the rarebit. Do not let it come to a boil.
After 5 to 7 minutes of constant stirring, the mixture should start to thicken noticeably as the yolks cook and the cheese fully melts. Keep stirring and do not let it boil. When the sauce is thick and smooth, stir in the butter, one piece at a time, and then the mustard. Remove the pan from the heat.
Toast the English muffins, then place 2 tomato slices on each half. Spoon the rarebit over each sandwich, reheating it first if it's not still hot (the sauce can become grainy as it cools). Garnish with parsley, if desired, and serve immediately. Makes 4 to 6 sandwiches.