Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish and set aside.

Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chopped yellow onion and cook for 3-4 minutes until softened. Add the sliced zucchini or yellow squash and sauté for 5-7 minutes, stirring occasionally, until the squash is slightly tender-crisp and has released some of its moisture. You don't want it mushy, just softened.

Stir in the minced garlic and cook for another minute until fragrant. Remove the skillet from the heat and set aside.

In a clean large skillet (or the same skillet wiped clean), melt 1/4 cup unsalted butter over medium heat. Whisk in the all-purpose flour and cook for 1-2 minutes, stirring constantly, to create a roux. This will thicken your sauce.

Gradually whisk in the milk and then the chicken or vegetable broth, ensuring no lumps form. Continue to whisk and cook for 5-7 minutes, until the sauce thickens to a creamy consistency.

Remove from heat and stir in the dried thyme, dried oregano, black pepper, and salt. Add the shredded sharp cheddar cheese and half of the grated Parmesan cheese (1/4 cup), stirring until completely melted and smooth.

In a large mixing bowl, gently combine the sautéed zucchini and onion mixture with the creamy cheese sauce, ensuring everything is well coated.

Pour the mixture into your prepared 9x13 inch baking dish, spreading it evenly.

In a small bowl, combine the panko breadcrumbs and 2 tablespoons of melted butter, stirring until the breadcrumbs are evenly coated.

Sprinkle the buttered panko breadcrumbs evenly over the squash mixture. Then, sprinkle the remaining 1/4 cup of grated Parmesan cheese over the breadcrumbs.

Bake for 35-40 minutes, or until the casserole is bubbly around the edges and the topping is golden brown and crisp.

Remove from the oven and let rest for 5-10 minutes before serving. Garnish with fresh chopped parsley, if desired.