Heat a small pot of water to boiling on high. Once boiling, carefully add the eggs and cook for exactly 6 minutes. Drain thoroughly and rinse under cold water for 30 seconds to 1 minute to stop the cooking process. When cool enough to handle, carefully peel the cooked eggs. Set aside in a warm place. Rinse and wipe out the pot.
While the eggs cook, wash and dry the fresh produce. Pick the sage leaves off the stems; discard the stems. Cut off and discard the mushroom stems; quarter the caps. Peel and roughly chop the garlic. Grate the cheese on the small side of a box grater.
In the same pot, combine 3 ½ cups of water and a big pinch of salt; heat to boiling on high. Once boiling, add the polenta; whisk to thoroughly combine. Reduce the heat to medium and cook, whisking frequently, 10 to 12 minutes, or until the water has been absorbed and the polenta has thickened. Turn off the heat.
While the polenta cooks, in a medium pan, heat a thin layer of oil on medium-high until hot. Once the oil is hot enough that a sage leaf sizzles immediately when added to the pan, add the sage in a single layer. Cook, stirring occasionally, 30 seconds to 1 minute, or until dark green and crispy. Leaving the oil in the pan, carefully transfer the fried sage to a paper towel-lined plate; immediately season with salt.
While the polenta continues to cook, heat the pan of reserved oil on medium-high until hot. Add the mushrooms and cook, without stirring, 2 to 3 minutes, or until browned. (If the pan seems dry, add 2 teaspoons of olive oil.) Season with salt and pepper. Continue to cook, stirring frequently, 1 to 2 minutes, or until softened. Add the garlic and spinach; season with salt and pepper. Cook, stirring frequently, 1 to 2 minutes, or until the spinach has wilted. Turn off the heat. Add the vinegar (be careful, as the vinegar may splatter) and half the butter; stir to thoroughly combine. Season with salt and pepper to taste.
Whisk the spice blend, half the cheese, and the remaining butter into the pot of cooked polenta until well combined. Season with salt and pepper to taste. (If the polenta seems too thick, gradually whisk in up to 2 tablespoons of water to achieve your desired consistency.) Divide between 2 dishes. Top with the cooked vegetables and sauce, remaining cheese, and peeled eggs. Season with salt and pepper. Garnish with the fried sage. Enjoy!