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Preheat oven to 325 degrees.
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In a large bowl, whisk together the flour, baking powder and salt.
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In another bowl, beat the butter until creamy (I use an electric handheld mixer) Add confectioners sugar and peanut butter, and beat until light and fluffy.
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Add the vanilla extract.
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Next beat in the dry ingredients at a low speed.
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Divide the dough into three portions, and shape into logs about 2-2 ½ inches in diameter.
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Wrap the three logs in plastic wrap and refrigerate until firm, at least 2-3 hours.
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Slice the logs into 1/3 disks, and arrange on cookie sheets lined with parchment paper.
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Place cookies about 1 apart.
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Bake each sheet in the oven for 20 minutes, or until just golden.
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If you prefer to do two sheets at a time, be sure to change the sheets from the top to bottom rack halfway through cooking.
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When cookies are removed from the oven, gently make a 1 ½ round indentation in the center of each one.
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(A shot glass works well for this) While the sheets of cookies cool, add chopped chocolate to a heatproof bowl.
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Next, slowly bring the heavy cream to a boil in a small saucepan, and pour over chopped chocolate.
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Let the chocolate melt a bit, and then whisk until smooth.
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After the ganache has cooled for a bit, spoon it into the cookie indentations (about a tsp).
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Cookies can be stored in an airtight container for a week.