Preheat the oven to 350 degrees F (175 degrees C).
Bring a stockpot of lightly salted water to a boil. Add the Cauliflower (1 head) and boil until the florets are tender but not mushy, 5 to 7 minutes.
Drain the cauliflower thoroughly. Place the cauliflower in the food processor.
In the frying pan, heat the Vegetable Oil (1/4 cup) over medium heat. Add the Onion (1) and sauté until translucent and lightly golden, 7 to 10 minutes.
Add the Mushroom (8 ounce), Kosher Salt (1 3/4 teaspoon), and Freshly Ground Black Pepper (1/4 teaspoon) and cook, undisturbed, for at least 1 minute to help the mushrooms darken.
Cook, stirring occasionally, until the mushrooms are browned and their liquid has evaporated, 5 to 7 minutes more.
Transfer the mushrooms and onion (and any extra oil from the pan) to the food processor with the cauliflower. Add the Egg (4) and Large Egg Yolks (3) and process until the mixture has a smooth consistency with minimal clumps.
Transfer the mixture to a large bowl, stir in the Matzo Meal (2 tablespoon), and mix well.
Grease six 8-ounce ramekins or a 9-inch glass baking dish.
Fill with the cauliflower mixture. Each ramekin should hold a little under 1 cup of the filling. Tap the bottoms of the ramekins or baking dish against the counter so that the top of the kugel flattens out and you’ve released any air bubbles.
Bake for 55 minutes to 1 hour. The kugel is done when a toothpick inserted into the center comes out clean and the kugel is lightly browned on top. Remove from the oven carefully and let cool slightly.
While the kugel is baking, slice the Shallot (4) as thin as possible.
In a small nonstick pan, heat the Grapeseed Oil (1/4 cup) over medium heat. Once the oil is hot, immerse the shallots in the oil and fry them, stirring frequently, until they are crispy, crunchy, shrunken, and dark in color, 15 to 20 minutes. Keep an eye on them to make sure they don’t burn.
Transfer the shallots to a paper towel-lined plate to drain and sprinkle lightly with salt. Set aside until serving.
Garnish the kugel with the fried shallots and the Fresh Parsley (to taste).