The Brioche Garnie is a smaller corner of French sandwich-making than the Croissant Garni or the baguette traditions, in part because brioche is sweet enough that it doesn't easily host savoury fillings. But the versions that have stuck are interesting precisely because they argue with the bread.
The Lyonnais Brioche aux Pralines is a regional dessert (pink praline-sugar baked into the dough) that gets re-purposed when split and filled with whipped cream cheese and herbs — sweet brioche, savoury filling, the sandwich tastes like Sunday brunch at someone's grandmother's. The Brioche Perdue Garnie is yesterday's brioche, French-toasted, then layered with thin-sliced ham and béchamel; it lives between sandwich and dessert and gets ordered late at night.
The more straightforward Brioche Jambon-Fromage uses a plain pain brioché — less sugar, more butter — and treats the bread like a softer, richer pain de mie. It's the sandwich that ends up in train-station lunchboxes and at children's school lunches, and the test of whether it's done well is whether the brioche keeps its structure after the cheese melts: too much enrichment and the bread becomes a wet shawl; just enough and it stays a sandwich.