Preheat oven to 350°F (175°C) and butter a 9×13 inch baking dish. Warm olive oil and 1 tbsp butter in a large skillet over medium-high heat. Add mushrooms, cook undisturbed 3 minutes, then stir and cook 5–7 minutes until liquid evaporates. Add a pinch of salt, garlic, and spinach, and cook until spinach wilts, about 2 minutes. Remove from heat.

Whisk eggs, milk, cream, Dijon, salt, and pepper in a large bowl until smooth.

Layer half the bread, half the mushroom mixture, and half the Gruyère and all the Parmesan in the dish. Repeat with remaining ingredients. Pour custard over top, pressing down gently. Let stand 10 minutes, pressing a few times.

Dot with remaining 1 tbsp butter and bake 45–50 minutes until golden and puffed, with a slight jiggle in the center. Let rest 10 minutes.

Slice into squares and serve warm.