Heat the oven to 180°C/350°F. Grease a medium baking dish.
Whisk together the eggs, milk, mustard, thyme, nutmeg, half of each cheese and plenty of salt and pepper. Spread the croissant pieces, ham and spinach in the baking dish then pour the egg mixture over them.
Top with the rest of the cheese then bake for 45 minutes until set in the middle. Leave to cool for 5 minutes then sprinkle with thyme sprigs before serving.
Nutrition information is an estimate and will vary depending on the exact ingredients used.