Place squash cubes & 1 tbsp of butter into a skillet over medium heat. Stir occasionally until cooked through (roughly 10 minutes) then remove from heat & set aside.
Melt remaining butter in a saucepan over medium-high heat. Add onion & garlic; cook & stir for 2 minutes until they begin to soften, then stir in the rice. Continue cooking & stirring until the rice is glossy from the butter, & the onion begins to brown on the edges, about 5 minutes more.
Pour in the white wine; cook, stirring constantly, until it has evaporated. Stir in ⅓ of the hot vegetable stock; reduce heat to medium. Cook & stir until the stock has been absorbed by the rice, 5 to 7 minutes. Add half of the remaining stock, & continue stirring until it has been absorbed.
Finally, pour in the remaining stock & butternut squash, & continue stirring until the risotto is creamy. Stir in the Parmesan cheese, & season to taste with salt & pepper. Finally top each individual serving with Pecorino Romano cheese.
To prepare sauce, in a large skillet combine 3 tbsp canola oil & flour little by little & mix to create a roux. Stir in flour to absorb the oil. Slowly whisk in the milk, & add Parmesan cheese & cheddar cheese. Stir in the egg to thicken the sauce, but do not allow to boil. Season with pepper, paprika, & Old Bay seasoning & remove from heat.
In a separate skillet, heat 2 tbsp canola oil. Saute mushrooms in the oil until soft.
In the same skillet, saute the asparagus.
Preheat the oven broiler. For each serving, put 2 slices of toast on a broiler-safe dish. Cover toast with layer of slices of turkey/pork roast & mushrooms. Smother each serving with sauce.
Place dish in broiler until the top of the sauce in speckled brown & bubbly. Remove from broiler, add tomatoes, & cross cross 4 stalks of asparagus (per serving) over top, & serve.
For each serving, slice up half an avocado & add as garnish.
Chef’s Note: The Kentucky Hot Brown retains a special place in my heart, as I was born in Kentucky. Of course, I had to add in more of a California flavor (and a dash of my Maryland side too) to make it healthier.