Add the cauliflower and parsnips to a large pot of salted boiling water. Cook to soften, 4 minutes. Drain and rinse under cold water in the sink.
Add the butter to a large saucepan or braising pan over medium-high heat. Once the butter is foaming, add the shallots and saute until tender, about 3 minutes. Sprinkle with salt and pepper. Stir in the flour and cook until pale blonde and pasty, 2 to 3 minutes. Slowly whisk in the warm milk, making sure no lumps from the flour remain. The sauce should begin to thicken up as it begins to simmer. Once the sauce becomes thick, turn the heat to low, and add the Cheddar in handfuls. Stir until melted and season with hot sauce. Add the drained cauliflower and parsnips into the cheese sauce and stir to coat.
Mix together the breadcrumbs, Parmesan, olive oil, parsley and some salt and pepper in a small bowl. Top the casserole with the breadcrumb mixture. Bake until bubbling and golden, 20 minutes. Let rest 5 minutes before serving.