1) Preheat the oven to 350°F. Lightly grease (or line with parchment) two baking sheets.
2) To make the cookies: Combine the sugars, peanut butter, shortening, salt, baking soda, and vanilla, beating until smooth.
3) Add the egg, beating to combine.
4) Stir in the oats and flour.
5) Drop the dough by the heaping teaspoonful onto the prepared baking sheets, leaving about 1 1/2" between them. A teaspoon cookie scoop works well here.
6) Using the flat bottom of a drinking glass dipped in sugar, flatten each cookie to about 1/4" thickness, about 1 1/2" diameter. If you're a fan of the popular sweet/salty flavor combo, sprinkle each cookie with the tiniest amount of extra-fine salt (or to taste; you know your own tolerance for saltiness).
7) Bake the cookies for about 12 to 14 minutes, until they're a medium golden brown.
8) Remove them from the oven, and transfer them to a rack to cool. Once they're cool, wrap airtight; they'll soften if left unwrapped.
9) Decide which type of filling you want to use. Each recipe makes enough to fill all the cookies.
10) To make the peanut butter filling: Mix all of the ingredients until smooth; a mini food processor works well here. If you're not using a food processor, sift the confectioners' sugar before stirring it together with the peanut butter and milk or half & half.
11) To make the fudge filling: Combine the chocolate chips and half & half in a small, microwave-safe bowl; or in a small saucepan. Heat until the half & half is steaming. Remove from the heat, and stir until the chips have melted and the filling is smooth; reheat briefly if necessary.
12) Spread the filling on half the cookies. Top with the remaining cookies.
Yield: about 22 filled cookies.