In a large skillet, warm olive oil over medium-high heat, add in shallots, turn heat down to medium, and stir and sauté till they soften. Add mushrooms, add 1/2 teaspoon of salt, and stir shallots and mushrooms together. Cook mushrooms with shallots until they are soft and browned, turning occasionally. This should take about 10 minutes. When the mushrooms are browned and most of their liquid has evaporated, pour in the red wine and stir in the chives, scraping up the brown bits on the bottom of the pan. Continue to sauté the mushrooms until the liquid has reduced and thickened. Taste and add salt and freshly ground black pepper as desired.

Heat oven to 375° F. In the bowl of a food processor outfitted with a whisk attachment, blend the eggs with salt until frothy. Add milk and mix well. Add the flour and mix until frothy and thoroughly incorporated, 1 to 2 minutes, scraping the sides of the bowl as needed. Pour the batter over the mushrooms. Sprinkle the top with the grated graviera. Grind a little black pepper over the top. Cover with foil and place the dish in the center of the oven. Bake until the center puffs, and the clafoutis is set, about 30 minutes. Remove the foil and bake for 10 more minutes, until the clafoutis turns golden. Serve warm or at room temperature.