Start by cubing your rustic baguette into 1-inch (2.5cm) pieces. Spread them in an even layer across your rustic ceramic baking dish. Ensure the pieces are slightly stale to properly absorb the liquids.

In a large skillet over medium-low heat, melt the butter and olive oil. Add your sliced green and white leeks. Sauté slowly for 8-10 minutes until they become tender and translucent, but not browned.

Evenly distribute the warm, aromatic leeks over the bread cubes in the baking dish. Toss gently so the leeks are mixed perfectly throughout the bread cubes.

In a large mixing bowl, crack the whole eggs and whisk until the yolks and whites are fully blended. Pour in the whole milk and heavy cream, whisking vigorously to create a smooth, homogenous liquid.

Stir half of the finely chopped fresh green thyme leaves, kosher salt, and black pepper into the egg mixture. Pour this set creamy savory egg custard mixture evenly over the bread and leeks in the baking dish.

Press down gently on the bread cubes with a spatula to ensure every piece is fully submerged. Let the casserole rest for at least 30 minutes at room temperature to fully hydrate the starches.

Preheat your oven to 375°F (190°C). Evenly scatter the shredded Gruyère cheese over the soaked bread, ensuring edge-to-edge coverage.

Bake uncovered on the middle rack for 40-45 minutes. Watch for the visual cues: the edges should be puffed, and the top features a thick layer of melted, bubbly, and beautifully browned Gruyère cheese.

Remove from the oven and let it rest for 10 minutes to allow the custard to fully set. Garnish the top with the remaining sprinkle of finely chopped fresh green thyme leaves before serving.