Toss together the garlic, poblano, cauliflower, mushrooms, salt, chili powder, olive oil, cinnamon, coriander, cumin and red pepper flakes on a rimmed sheet tray in a single layer. Roast the vegetables until browned and tender, 10 to 12 minutes.
Carefully transfer the vegetables to a large pot and stir in the beans, tomatoes, BBQ sauce and hot sauce. Bring the mixture to a boil, stirring occasionally, then reduce the heat to medium low and simmer until the desired thickness, about 20 minutes total. Add a bit of broth or water for a looser chili.
For the pizza: Reduce the oven to 425 degrees F. Grease a rimmed half-sheet tray with the canola oil.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda and salt. Whisk in the eggs, buttermilk and melted butter until combined.
Pour the batter onto the prepared sheet tray. Transfer to the oven and bake until the top is light brown, 6 to 8 minutes. Remove the pizza from the oven and top with the chili and Cheddar, leaving a 1/2-inch border around the crust. Bake until the cornbread is done and the cheese is melted, about 10 more minutes.
Allow the pizza to cool slightly before slicing and serving. Top with jalapenos, sour cream and cilantro as desired.