Oh shit, galette complète oeuf miroir*, the chef knows what's up. Truly one of the best, in spite of being nearly as simple as it can be. For precision, it's quite unlike sweet galettes, since sweet galettes are usually with something more like puff pastry, including the more common in France (especially in early January) galette des rois which is basically puff pastry filled with frangipane, an almond-based sweets filling.
It's more of a dish from Brittany, where galettes are very much common. They're pretty much crepes, except simpler. Pretty much just buckwheat flour and water (some salt for taste, and some add an egg for color, but never did that). There's also some parts of Brittany (I think south and west) which claim that buckwheat galettes and crepes co-exist and that akchually galettes are thicker, but that seems to not gbe acknowledged by the majority, and possibly is a very local differenciation that isn't widely shared.
Anyway, the most two famous ways to eat a galette would be the complète as shown here, or the simpler but kinda more filling galette saucisse, which as its name imply, is just a galette wrapped around a sausage.
*Oeuf miroir (mirroregg) means sunny-side up. Other common way to ask for the egg would be oeuf brouillé, literally scrambled eggs. It cooks faster and you can close the galette and flip it for cooking both sides.