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For the ganache: Place the chocolate in a glass or metal bowl. Scald the cream in a small saucepan until the edges are just starting to bubble. Do not bring to a boil. Pour the cream over the chocolate and let sit for a moment to melt the chocolate. Slowly stir to incorporate the cream and chocolate. (The mixture should start to thicken up as the chocolate melts.) Refrigerate the ganache until it has thickened to the consistency of warm peanut butter.
For the financiers: Preheat the oven to 375 degrees F.
Heat 3/4 cup of the butter in a small saucepan over medium-high heat, swirling the pan occasionally until the butter begins to bubble and brown. Set aside to cool.
Using a pastry brush, spread the 3 tablespoons of melted butter in the cups of the muffin tins. Set aside.
Carefully fill the muffin tins two-thirds of the way with the batter. Bake for 4 minutes to begin to set the financiers.
Meanwhile, fill a small pastry bag with the chocolate ganache.
Pull the muffin tins from the oven, squeeze a small amount of ganache into the center of each cake and return to the oven. Reduce the oven temperature to 350 degrees F and bake until the financiers are slightly golden brown and the top of the cakes spring back when lightly pressed, about 8 to 10 minutes more.
Cool the cakes for at least 10 minutes before serving.