Spray two medium bowls with nonstick cooking spray; set aside.
In separate bowl, whisk together Bread Mix, yeast, sugar, and salt; set aside.
In bowl of stand mixer with paddle attachment, mix together eggs, milk, water, and oil until evenly blended. Add flour mixture and beat on medium speed for 3 minutes, scraping down sides to incorporate all ingredients into dough. Divide dough evenly between the two prepared bowls and smooth top of dough with oiled spatula. Cover bowls and place in warm, draft-free spot about 30 minutes, until dough is starting to rise and look puffy.
Place large sheet of parchment paper on work surface and heavily dust it with flour. Flour surface of dough in one of the bowls. Flour one hand and flip floured side of dough into your floured hand, and then onto the center of the floured parchment. Using heavily floured fingers, slowly press dough outward from the center to form 9-inch circle, being sure not to make the center too thin (circle should be the same thickness throughout), and adding flour as needed to keep from sticking.
Heavily dust dough circle with flour, then place another piece of parchment paper on top, and use both hands to gently flip dough over, using your arm for support while flipping. Remove top piece of parchment paper, and again sprinkle dough and the exposed parchment paper heavily with flour. Repeat process of pressing dough circle out, starting in the center and working to the edge, to form a thinner, larger circle. Flour dough again, cover with parchment paper, and gently flip. If needed, slide extra parchment paper under edges of dough. Peel parchment paper off, flour top of dough and the surrounding exposed parchment paper, and press dough out again into a 13-inch circle. Brush excess flour off with a small brush, put fresh sheets of parchment paper on top and flip one more time. Brush the flour off the second side.
With a floured pizza cutter or knife, cut circle into four quarters. Cut those quarters in half to form 8 equal pie wedges. With a pie server or metal spatula, pull out one piece at a time, set it onto a floured surface, and cut that slice in half to make two skinnier wedges. Brush each piece gently to remove more flour, sprinkle with cheese (if using), and roll up from the wide end towards the point. Gently lift roll and place seam side down (point on the bottom) onto sheet pan lined with parchment paper. Repeat for all the pieces, to make 16 rolls, and set aside to rise in warm draft-free place for about 1 hour. They should puff a bit as they rise and will continue to rise while baking. Repeat entire process with other half of dough.
Preheat oven to 350° with rack in center. Bake rolls for about 20 minutes, until starting to brown. While rolls are baking, melt butter. As soon as rolls come out of oven, brush with melted butter. Rolls are best served warm out of oven.
To make rolls ahead of time for baking later in the same day: After making rolls but before letting them rise, spray tops of rolls lightly with nonstick cooking spray and loosely cover with plastic wrap. Put them in refrigerator until 90 minutes before baking. Remove from refrigerator, uncover, and set in warm, draft-free place for about 90 minutes, then bake as directed.
To freeze rolls ahead of time for baking another day: After making rolls but before letting them rise, spray tops of rolls lightly with nonstick cooking spray and tightly wrap pan with plastic wrap. Put pan in freezer. Before baking, put frozen rolls in refrigerator to thaw for about 6 to 8 hours, then loosen plastic wrap, and let rolls rise in warm, draft-free spot for about 90 minutes, until puffy; bake as directed. Alternatively, remove pan from freezer, loosen plastic wrap, and set directly on counter in warm, draft-free spot 2 to 2½ hours, until puffy; bake as directed.
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