Prepare the namul (soybean sprouts, spinach, carrot, mushrooms) and the protein exactly as you would for regular bibimbap, and set each aside separately.
Set the empty stone bowl over medium heat for 5 to 8 minutes, until a flicked drop of water skitters across the surface rather than sitting and boiling.
Brush the inside generously with 2 tbsp sesame oil, all the way up the sides — more than looks reasonable.
Press the warm rice into the bottom in an even layer, working quickly since the bowl is already hot underneath it.
Arrange the namul, protein and egg on top and leave the bowl completely alone over medium-low heat for 3 to 4 minutes, listening for a faint crackle from underneath.
Loosen the sauce ingredients together until they ribbon off a spoon, then take the bowl off the heat.
Bring it to the table still sizzling, spoon over the sauce, and mix at the table, scraping the crust up from the bottom as you go.