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In saucepan, warm milk, water and sugar together until about 110 degrees F. Stir in yeast and let it sit until foamy, about 5-7 minutes.
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In large bowl or in bowl of stand mixer, mix together flour and salt.
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Into saucepan with yeast mixture, add melted butter and egg.
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Pour liquid mixture into flour mixture. Using stand mixer or hand mixer, mix on low speed, then increase to medium-high, until dough is smooth and elastic, about 7 minutes.
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Lightly oil a mixing bowl and transfer English muffin dough. Cover and let rise until doubled in size, about 1 hour.
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On floured work surface, gently pat dough to just under 1-inch thick. Dust two baking sheets with semolina or cornmeal.
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Cut dough into rounds using 3-inch cutter and place cut-outs on prepared sheets. Cover loosely and let rise again about 30 minutes.
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Heat skillet or griddle over very low heat. Sprinkle semolina or cornmeal on cooking surface. Arrange dough rounds on griddle or skillet, cover, and cook 5-6 minutes per side, until golden-brown and cooked through.