Preheat the oven to 350 degrees F (175 degrees C). Grease 36 mini muffin cups.
Combine sugar and 2 tablespoons plus 1 teaspoon lemon zest in a bowl. Rub sugar and lemon zest with your fingers until sugar is moist and fragrant. Add butter and beat with an electric mixer until creamy. Add egg and beat well. Mix in flour, baking soda, and salt until incorporated.
Fill each mini muffin cup 3/4 full of dough.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 12 to 15 minutes.
Use a spoon to flatten any cookie cups that have risen over the rim of the tins. Make a well in the center of the warm cookie cups with your finger or a small spoon. Chill cookie cups, still in the tins, for 30 to 60 minutes.
Meanwhile, beat cream cheese and butter together until smooth. Add lemon juice and zest. Beat in powdered sugar until frosting is fluffy.
Remove cold cookie cups from the tins. Spoon 1/2 teaspoon raspberry jam into each one. Pipe frosting on top of the jam to cover it completely. Add a dot of raspberry jam to the center for a pretty presentation, if desired.