Preheat oven to 275°F. Spray standard muffin tins lightly with nonstick spray. Line 15 of the muffin cups with paper liners. Place 1 whole peanut butter cup in the bottom of each.
In the bowl of an electric mixer, beat the cream cheese on medium-high speed until smooth. Gradually add the sugar and beat until combined. Beat in vanilla. Beat in eggs, one at a time, until combined. Beat in sour cream and salt. Stir in chopped peanut butter cups with a rubber spatula.
Divide batter evenly among prepared muffin cups. Bake until filling is set (no longer thin and liquid-looking), about 22 minutes. Transfer to wire racks to cool completely. Refrigerate for at least 4 hours or overnight before removing cupcakes from tins to serve.