In a small pot, combine the milk and flour. Set over medium low heat and whisk, cooking until thickened. Remove from the heat and set aside.
In the bowl of a stand mixer, add the warm water and sprinkle the yeast over it. Add a pinch of the sugar and stir. Let the yeast bloom for about 5 minutes: the mixture will turn frothy and bubbly.
Add the flour, the rest of the sugar, the egg, and salt, then the roux (thickened flour paste) and the discard. Affix the dough hook and knead until the dough starts coming together in a ball around the dough hook, about 5 minutes. Add the softened butter and knead until you have a smooth, elastic dough that clears the sides of the bowl, about another 5-7 minutes.
Transfer to an oiled bowl and toss the dough around to coat in the oil. Cover to seal with plastic wrap and set aside until almost doubled, the dough should be puffed. Depending on how active the starter was and how warm your kitchen is, this can take 2-4 hours.
Grease an 8 or 9 inch square or round pan. Turn the dough out of the bowl onto a floured surface and divide into 12 pieces. Roll each piece into a ball and arrange in the pan, leaving a bit of space between each dough ball. Cover with a tea towel and let rise until puffy and when gently pressed with a finger, the dough leaves an indentation (does not bounce back immediately). This can take 1-2 hours depending on how active the starter was and kitchen temperature.
Preheat the oven to 375 F. Bake the rolls for about 30 minutes, until deeply golden on top. A thermometer inserted into the center of the middle roll will indicate doneness when it says 190 F. Straight out of the oven, brush the rolls with some melted butter and sprinkle with flaky sea salt.
Rolls are best the day of, store leftovers in an airtight container. To soften, reheat in the microwave for 30 seconds.