- Heat the oil in a large sauté pan over medium heat. Add the onions and thyme and sauté until they are soft and tender, about five minutes. Add the spinach and stir until it is wilted and add the vermouth (if using). Remove the pan from the heat to cool about ten minutes. Season to taste.
- Preheat the oven to 350 °F and grease a 22 centimeter springform pan (or oval baking dish). In a large bowl, whisk the eggs, mustard, salt & pepper and whisk in the milk. Add the bread cubes and toss well to coat. Let this sit for 15 minutes to allow the bread to soak in the liquid. Stir in the cooled onion and spinach mixture as well as the diced ham, and then stir in the diced brie. Bake the strata for 60 to 70 minutes, until the centre springs back when gently pressed. Allow the strata to cool for 15 minutes before removing from the pan (if baking in a springform pan)
- For the glaze, stir the mustard and maple syrup together. Brush this over the top of the warm strata and then use any remaining as a sauce when serving.
The strata can also be assembled and baked a full day ahead, and reheated for 30 minutes, covered, in a 325 °F oven, or it can be assembled the evening before, kept chilled and baked fresh the next morning.