Combine 2 cups flour, sugar, Fleischmann's® RapidRise Yeast and salt in a large mixer bowl.
Heat milk, water, and 1/4 cup butter until very warm (120° to 130°F). Stir into flour mixture. Beat 2 minutes at medium speed with an electric mixer, scraping bowl occasionally.
Add the egg and 1/2 cup more of the flour. Beat for 2 minutes at high speed. Stir in enough remaining flour to make a soft dough.
Knead on a lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes. (Or, if desired, place dough in a greased bowl, cover with plastic wrap, and allow it to rise in the refrigerator for 12 to 24 hours.)
Divide dough in half; roll each half to a 12-inch square, about 1/4-inch thick. Cut each into 6 (12 x 2-inch) strips. Cut each strip into 3 (4 x 2-inch) rectangles. Brush each rectangle with melted butter and sprinkle with Everything bagel seasoning. Arrange in rows ¼ inch apart to allow room to expand. Cover and let rise in a warm place for 30 minutes or until doubled in size.
Once rolls are proofed, preheat the oven to 400°F. Bake the rolls for 13 to 15 minutes or until golden brown and hollow sounding when you tap on the bottom of a roll.
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