Combine the warmed non-dairy milk, instant yeast and sugar in the bowl of a stand mixer. Add the flour, sourdough discard, beaten egg and salt. With the mixer on low, slowly pour in 2 Tablespoons of melted butter. Increase speed to medium and mix until a shaggy dough forms, about 2 minutes.
Transfer the dough to a smooth work surface and knead until a smooth dough forms, about 3-4 minutes. Dough should be smooth and slightly tacky (not sticky). If needed, add more flour or non-dairy milk (1 Tablespoon at a time) to reach your desired consistency.
Transfer the dough to a large oiled bowl and cover with plastic wrap. Let rise for about 90 minutes, or until doubled in size.
Brush an 8x11-inch baking dish with 1 Tablespoon melted butter and set aside.
Turn the dough onto a smooth work surface and divide into 12 equal-sized pieces. This doesn't have to be exact, but if you do want perfectly identical rolls, weigh the dough and divide that number by 12 to determine how much the dough for each roll should weigh. Roll each piece of dough into a ball in the palm of your hand, then place the rolls into the prepared baking dish. Repeat until you have 12 rolls.
Cover the baking dish with plastic wrap and let the rolls rise for 60 minutes, until puffed and doubled in size.
Preheat the oven to 375℉. Brush the rolls with 2 Tablespoons melted butter, then sprinkle with flaky sea salt. Bake for 20-25 minutes until golden brown. If desired, brush with additional melted butter before serving.
