In a large pot over medium high heat, melt the butter then add the leeks, broccoli, and garlic. Cook while stirring for 3-4 mins until starting to become tender.
Add the zucchini, salt, pepper, and oregano. Cook while stirring for 5-6 more mins until almost fully tender.
Turn the heat down to medium and add the spinach. Cook for 2-3 mins until bright green and wilted.
Preheat the oven to 375F.
In a separate medium pot over medium heat, melt the butter and then add the flour. Cook the flour while whisking constantly for 1 min.
Gradually add the milk ½ cup at a time, whisking so that the milk gets fully incorporated before adding more.
Once all of the milk is added, turn heat up to medium high and cook, whisking often, until the sauce starts to bubble and thickens slightly (4-6 mins).
Mix in the kosher salt, pepper, nutmeg, cayenne, and parmesan.
