Salty, savory miso gives this veggie noodle dish more complex flavor.
Bring a large pot of water to a boil for the udon.
Arrange a rack in the upper third of the oven; preheat to 450°. Line a baking sheet with parchment paper. Arrange the shallot and maitakes in a single layer on the parchment. Spray with the cooking spray and season with the shichimi togarashi. Roast until the mushrooms are tender and crispy at the edges, 15 minutes.
Add the udon to the boiling water; cook until al dente. Drain and rinse under cold water. Transfer to a bowl and drizzle with about 1 1/2 tsp. oil.
In a large pot, heat the remaining oil, two and a half turns of the pan, over medium-high. Add the shiitakes and cook, stirring often, until browned in spots, about 5 minutes.
Add the chard stems, leek, garlic, and ginger to the pot with the shiitakes; season with white pepper. Add the mirin, miso, and tamari, then add the stock. Bring to a simmer. Add the chard leaves and cook until wilted, 1 to 2 minutes. Stir in the sesame oil; season.
Divide the udon among bowls. Ladle the broth and mushrooms on top. Garnish with the sesame seeds and roasted shallots and mushrooms.