Prepare all the ingredients and start by cooking the onions over medium-high heat until they begin to brown. Use an oven-safe pot.

Add the carrots and stir. Cook over medium heat for 4-5 minutes. In another oven-safe pot, start cooking the broccoli. Cook until they are softened and slightly browned.

When the carrots have softened, add the mushrooms. Cook, stirring, for 4-5 minutes.

Add the sliced leeks and ham. Stir. Lower to medium-low heat. When the broccoli is ready, add it as well.

Prepare the béchamel sauce: Melt the butter and add the onions. Cook for 2-3 minutes until they are translucent. Add the flour and quickly whisk. Let the mixture (a "roux") cook over medium heat for 2-3 minutes.

Continue with the béchamel: Add the milk and whisk vigorously to prevent lumps from forming. Bring to a boil over medium-high heat, then reduce to medium heat. Stir constantly to achieve a smooth texture. The sauce should thicken after 1-2 minutes and continue to thicken afterward. Once the sauce is stable, add the cheese and stir to incorporate. Set aside, stirring occasionally to maintain a uniform texture.

Distribute the vegetable and ham mixture into the two pots. Add the pasta and béchamel sauce. Mix well to combine evenly. Cover with the cheese slices.