Prepare the mushrooms. Wipe excess dirt from the mushrooms with a damp cloth or paper towel. Roughly chop into 1/2-inch to 1/4-inch pieces.

Cook the mushrooms. Melt butter in a large saucepan over medium high heat. Add shallots and cook until soft (about 3 minutes). Add mushrooms and cook, stirring frequently, for about 5 minutes. Add white wine, reduce heat to medium, cover and cook for 5 minutes. Uncover the pot and continue to cook until most of the liquid is gone, stirring occasionally (about 2 more minutes). Add cream, stirring to combine. Cook until the mixture thickens up a bit (about 2 minutes). Season to taste with kosher salt and freshly ground black pepper.

Assemble and serve. Top each crostini with a spoonful of mushroom mixture. Sprinkle with chives and flaky sea salt then serve.