Preheat the oven to 400℉ and lightly grease a baking dish with oil.
Heat olive oil in a medium saucepan over medium heat. Add diced onion and minced garlic, season with salt and pepper, and cook for 4 to 5 minutes until softened and fragrant.
Stir in quinoa and dried dill. Cook for 2 to 3 minutes to lightly toast the quinoa.
Pour in vegetable broth and bring to a boil. Reduce the heat to medium-low, cover, and simmer for 12 minutes. Remove from heat and let sit covered for 5 minutes.
Fluff the quinoa, then stir in broccoli florets. Add heavy cream and shredded white cheddar. Stir until the cheese melts and the mixture becomes creamy. Taste and adjust seasoning.
Transfer the mixture to the prepared baking dish and spread evenly.
In a small bowl, mix breadcrumbs, melted butter, and parmesan cheese. Sprinkle evenly over the top.
Bake for 10 to 15 minutes until the top is golden brown and the gratin is bubbly. Remove from oven and finish with fresh parsley before serving.