For the caramelized onions: Warmth a big Dutch oven or braiser over medium warmth. Add the olive oil adopted by the sliced onions and salt. Stir to coat, then cook dinner till the onions soften, about quarter-hour. Scale back the warmth to medium-low/low and proceed to cook dinner, stirring often, till the onions are a deep golden shade, about 1 hour. Stir within the vinegar and cook dinner for an additional quarter-hour—the onions ought to proceed to deepen in shade.
For the filling: As soon as the onions are caramelized, stir within the broth, thyme, Worcestershire sauce, dietary yeast, and shiitake powder. Cook dinner for a couple of minutes, till the combination thickens barely. Flip off the warmth, take away the thyme sprigs, and let the filling sit whereas getting ready the dough.
To make the galette: Preheat the oven to 425˚F. Roll the ready dough right into a 12” circle on a floured floor. Switch to a baking sheet lined with parchment paper. I prefer to take a 8” plate, flip it the wrong way up, and gently lay it on the dough to go away an indentation to information the interior circle. The purpose is to go away about 2” across the fringe of the dough.
Use a pointy knife to chop slits each 3-4” alongside the two” dough border. Sprinkle on 2 ounces of the cheese and spoon the onion filling over the cheese, spreading it out to the sides of the interior circle.
In a small bowl whisk the egg till frothy. Take one of many border sections of dough and fold it over the filling. Brush with the egg, then repeat with the following part of dough, overlapping it barely with the earlier part. Proceed on this vogue all the way in which across the dough border.
Bake the galette for 20 minutes, sprinkle with the remaining cheese, then bake for 20 minutes extra, till the crust is crisp and golden and the filling is effervescent. Pull from the oven, crack some black pepper on high, and wait about 10 minutes to chop and serve.
