Preheat oven to 325 degrees F.
Peel the onions by trimming the top and dropping them in a pot of boiling water for 30 seconds. Remove from the water, rinse to cool, then peel the outer layer of skin. While the onions are cooling, you can wash and slice the mushrooms into thick slices, about the width of your thumb.
First, roast the vegetables. Place the tomatoes, whole peeled onions, mushrooms, and whole garlic cloves on a parchment lined baking tray and drizzle with the olive oil, salt, and pepper, and toss to evenly coat all the vegetables.
Place the vegetables in the oven for one hour. You want the tomatoes to be blistered and wrinkled but still hold some shape.
While the vegetables are roasting, make the arugula pesto by combining all of the pesto ingredients in a food processor and pulsing until completely combined. It will still have some texture but you shouldn't have unchopped pieces of greens or nuts.
When you have about 15-20 minutes left for the vegetables, you can start the polenta. Bring the water and plant milk to a low boil in a pot for which you have a lid then pour in the cup of polenta, stirring with a whisk as you do to avoid clumping. Add the baking soda and salt, and stir well. Cover the pot, turn the heat to the lowest setting, and let cook for 15 minutes, stirring every 5 to make sure the polenta doesn't stick.
After 15 minutes, add the plant butter, vegan parmesan, and nutritional yeast and stir until completely combined, another minute or two. Then remove the pot from the heat, and stir in the herbs.
Serve the dish by spooning a generous helping of polenta, then the pesto, then topped with the roast veggies. Add some lemon zest and a squeeze of lemon juice of the top to serve!