In a large saute pan over medium heat, melt butter. Add the shallot and garlic, stirring constantly for 1 minute. Add the chopped mushrooms. Cook until the mushrooms begin to soften, about 5 minutes. Transfer the mushroom mixture to a food processor and add the goat cheese. Add the oil and parsley. Pulse until the mixture comes together. Season with salt and pepper and pulse again.
Spoon mushroom filling into tartlet shells and place on a baking sheet. Bake in a preheated 350 degree oven for 10 minutes. Garnish with sliced mushroom and chopped chive before serving.