In a medium pot with a tight-fitting lid, combine wild rice, 2 cups water and a pinch of salt. Bring to a boil over high heat, top with lid and reduce to low. Cook 45 minutes. Fluff with a fork, remove from heat and cover. Let steam 5 minutes more. Divide among four serving bowls.
Place sunflower seeds on a rimmed baking sheet. Drizzle with 2 teaspoons olive oil, season generously with salt and pepper and sprinkle with cayenne. Toss to coat and transfer to oven. Roast until toasted and fragrant, about 10 minutes, stirring halfway through. Remove from oven and let cool.
Preheat a large skillet over high heat. Add 2 tablespoons olive oil and swirl to coat. Add half of the mushrooms, season with salt and pepper, and cook, stirring only occasionally until golden, about 5 minutes. Remove mushrooms to a plate and repeat with 2 tablespoons olive oil and remaining 1/2 pound mushrooms. Return all mushrooms to the pan. Make a well in the center and add remaining 1 teaspoon olive oil and garlic. Saute until just beginning to turn golden, about 2 minutes. Fold to incorporate all mushrooms and add sherry vinegar, scraping bottom of pan to deglaze, cooking 1 minute more. Season to taste with salt and pepper and divide among serving bowls with rice.
Place tofu slices on a rimmed baking sheet. Drizzle each slice with 1/4 teaspoon sesame oil and 1/2 teaspoon sesame seeds. Season tops with salt. Transfer to broil and cook until sesame seeds are toasted and tofu pieces are golden on the edges, about 8 minutes. Divide among serving bowls with rice and mushrooms.
Meanwhile, bring a medium pot of water to a boil over high heat. Add rice wine vinegar and season water with salt. Reduce heat to a brisk simmer. Crack eggs into small ramekins and tip each one into a different corner of the pot. Maintain a simmer and cook eggs just until whites are set, about 3 minutes. Remove with a slotted spoon to a paper towel-lined plate to drain.
Divide kale, cucumbers, radishes, sunflower seeds and poached eggs among serving bowls. Top with Miso-Ginger Dressing and serve.
For the Miso-Ginger Dressing:
In a medium bowl, whisk to combine miso and rice wine vinegar. Add olive oil, sesame oil, honey and ginger and whisk until smooth. Add salt to taste. Dressing can be kept in refrigerator for up to 2 weeks.