Potato Leek Gratin

In the past, I've had trouble with runny gratins. So this time, I tried making a béchamel sauce with the milk and flour, rather than pouring/sprinkling it over the assembled dish. This helped enormously. The texture and end result were exactly what I've always wished my gratins would be.

2 large leeks (white and light green parts only)
1 tablespoon fresh thyme leaves
3 tablespoons butter
2 tablespoons flour
1 cup milk
salt, pepper
3 russet potatoes, sliced very thinly
1 carrot, cut into tiny cubes
1/4 cup grated Parmesan cheese

Preheat the oven to 400 degrees.

Slice the leeks lengthwise, then crosswise into thin half moons. In a large saucepan over medium heat, melt the butter, then add the leeks and thyme and cook until the leeks soften, about 10 minutes. Push the leeks off to the side and whisk the flour into the butter. Cook for a minute or so then add the milk, whisking until the sauce thickens. Stir the leeks in, season with salt and pepper, and remove from heat.

Spoon a little sauce in the bottom of a medium baking dish. Then add a layer of potatoes and some of the carrots. Layer more sauce, more potatoes and carrots until all is finished off. Cover the top with the cheese and bake, covered, for about 30 minutes, then uncovered for another 25 or so minutes, until the potatoes are tender and the cheese is golden brown.