Season brisket with salt. Wrap tightly in plastic and chill at least 8 hours.
Let brisket sit at room temperature 1 hour.
Preheat oven to 400°F.
Combine mustard, brown sugar, and ginger in a small bowl. Unwrap brisket, place on a wire rack set inside a large rimmed baking sheet, and rub mustard mixture all over brisket. Roast until top is nicely browned, 30–40 minutes.
Remove brisket from oven and reduce oven temperature to 300°F.
Meanwhile, heat bacon fat in a large heavy ovenproof pot over medium heat.
Add onions; season with salt and cook, stirring often, until deep golden brown, 8–10 minutes. Reduce heat to medium-low, add flour, and cook, stirring often, until mixture smells nutty, about 4 minutes.
Add bay leaf, ale, and stock. Bring to a simmer.
Add brisket, cover, and transfer to oven. Braise, turning every 30 minutes, until fork-tender, 3–4 hours. Discard bay leaf.
Transfer brisket to a cutting board and let rest at least 20 minutes.
If braising liquid is thin, bring to a boil, reduce, and simmer, skimming surface as needed, until thick enough to coat a spoon; season with salt, if needed. Slice brisket against the grain.
Serve with braising liquid.
DO AHEAD: Brisket can be braised 2 days ahead. Cover and chill in braising liquid.