Prepare the mushrooms by shredding them lengthwise with a fork to create a pulled texture, or slice them into ½-inch thick rounds.
In a bowl, combine the mushrooms with the BBQ dry rub and 3 tablespoons (45 ml / 1.5 fl oz) of the oil.
Toss to coat evenly and set aside to marinate for at least 30 minutes (or up to 4 hours in the refrigerator).
To start the grits, heat a saucepan over medium heat.
Add the remaining 3 tablespoons (45 ml / 1.5 fl oz) oil, half (2 tablespoons / 30 ml / 1 fl oz) of the garlic, and half (2 tablespoons / 30 ml / 1 fl oz) of the shallots.
Cook, stirring frequently, until translucent, about 3 to 5 minutes.
Add the vegetable stock and bring to a boil.
Add the cooked grits and cook, stirring constantly, until the stock has been absorbed and the mixture is thick, about 10 minutes.
Set aside.
Heat a large sauté pan over high heat.
Add the marinated mushrooms in a single layer (work in batches if needed) and sauté until golden brown and slightly crispy, about 4 to 5 minutes per side.
Add the remaining 2 tablespoons (30 ml / 1 fl oz) garlic and 2 tablespoons (30 ml / 1 fl oz) shallots, and cook until fragrant, about 1 minute. Deglaze the pan with the white wine, scraping up any browned bits.
Then add the tomato, swirl in 2 tablespoons (30 ml / 1 fl oz) of the butter, and season with salt and pepper.
Set aside.
Return the grits to medium heat.
Add the cream in ¼-cup increments, stirring constantly, until the texture is smooth and creamy.
Stir in the white cheddar cheese, the remaining 2 tablespoons (30 ml / 1 fl oz) butter, and the fresh parsley; heat through until the cheese is melted.
Season to taste with salt and pepper.
To serve, spoon the cheesy grits into 2 to 4 serving bowls and top with the smoky mushrooms.
Garnish generously with the sliced scallions.
Don't rush the grits.
Stir them constantly as you add the cream to prevent lumps and achieve the smoothest, most luxurious consistency.