Make the crust: if you have a food processor, this makes it much easier. Pulse the flour, salt, pepper, and sugar until blended, about 4 or 5 pulses. Add the cold butter and cheese and pulse to combine. (See Notes if you do not have a food processor.)
Add 4 tablespoons of the cold water and pulse to combine. Continue to add cold water, one tablespoon at a time until the dough begins to come together into a ball.
Remove the dough from the processor and form into a ball, then flatten into a disc, about 8" in diameter. (It does not have to be exact.)
Wrap in plastic wrap and refrigerate for 2 hours or up to 2 days (or freeze for up to a month.)
Preheat the oven to 375 degrees.
Once chilled, remove the dough from the refrigerator and place the disc on a lightly floured work surface. Lightly flour the top of the dough also. Using a rolling pin, roll the dough to about a 12" round.
Transfer your rolled dough onto a piece of parchment paper big enough for the dough and place it on the cookie sheet, approximately 12"x15" sheet. Set aside while making the filling.
Make the filling: Place the sliced sweet potatoes in medium bowl and toss with the peppers, adobo sauce, black pepper, oil, and salt. (I used a disposable glove to make this a little easier to get in between all those layers of sweet potato.
Once all the ingredients are combined, layer the potatoes in the center of the galette dough, leaving a 2 1/2" border of the dough to fold over.
Begin anywhere around the edge and fold the dough over the edges of the filling, fold all the way around so that the filling is encased by the dough.
Using a pastry brush, brush your egg wsh on the surface of the edge of the dough that you just folded over.
Place the cookie sheet in the preheated oven and bake for 45 to 55 minutes.
Begin checking for doneness of the potatoes and nice browning of the crust at 45 minutes. Depending on your oven, it may take more or less time. The time listed is a guide. If your oven runs on the hotter side, you may want to begin checking at 40 minutes.
Once your sweet potatoes are tender enough to be pierced with a knife and the crust is nicely browned, remove from the oven. Allow the galette to cool for 10 minutes. Slice and serve. (Allow to cool longer if you prefer; it is still good at room temperature.)
If you happen to have any leftovers, store them covered in an airtight container in the refrigerator for up to 3 days.