Toast your sourdough bread, brush on some quality extra virgin olive oil or generously spread with quality butter, slice each piece in half, then set aside on the serving plates.
In a large frying pan or skillet over low heat, pour in a tablespoon of olive oil and heat, and fry the finely chopped shallot and garlic just until the shallot is soft and garlic is fragrant. Take care not to over-cook the shallot and garlic as you don't want them to burn while the mushrooms are cooking.
To the pan, add the rest of the olive oil and butter, increase the heat to medium, and add the mushrooms to the pan. Note: you don't want to crowd the mushrooms in the pan, so if you don't have a large pan, you can cook the mushrooms in batches. If using a mix of sizes, add the large mushrooms first, then the medium mushrooms, and small mushrooms.
Sauté the mushrooms: at first, use a wooden spoon or spatula to stir the mushrooms continuously but gently, so that they're covered in olive oil and butter, the shallots and garlic are evenly distributed, and the mushrooms evenly cook.
Once the mushrooms are fully coated and shallots and garlic evenly distributed, stir the mushrooms occasionally, allowing them to rest a little so the juices are released, the mushrooms soften, and they start to brown in places.
After a few minutes, or whenever the mushrooms are soft and brown, add a dollop of sour cream, 2 tablespoons of fresh dill (or other fragrant herb of your choice), a pinch of sea salt and freshly ground cracked black pepper to your taste. Stir to combine well.
Tip the mushrooms out of the pan and pile them onto the toasted sourdough, evenly distributing between plates.
Garnish with more fresh herbs and generously sprinkle with grated Parmigiano-Reggiano and serve immediately.