PREHEAT OVEN TO 350 DEGREES FAHRENHEIT. LINE COOKIE TRAYS WITH PARCHMENT PAPER OR A SILICONE BAKING MAT.
IN A LARGE BOWL, WHISK TOGETHER THE FLOUR, COCOA POWDER, BAKING SODA, BAKING POWDER, AND SALT. SET ASIDE.
IN A STAND MIXER WITH THE PADDLE ATTACHMENT, CREAM THE BUTTER WITH THE SUGARS. ADD THE EGG, VANILLA, AND MILK. MIX COMPLETELY. SCRAPE BOWL.
ADD THE DRY INGREDIENTS TO THE WET INGREDIENTS AND MIX COMPLETELY. DOUGH WILL BE THICK.
SCOOP ABOUT 1 TBSP OF COOKIE DOUGH (THE SIZE OF A QUARTER), ROUND DOUGH INTO A BALL, AND PLACE IT ONTO THE PREPARED COOKIE SHEETS A FEW INCHES APART. (12 COOKIES PER HALF SHEET TRAY. YOU SHOULD GET CLOSE TO 36 COOKIES TO MAKE 18 SANDWICH COOKIES.)
USE THE BOTTOM OF A MEASURING CUP TO PRESS THE COOKIE DOUGH BALLS HALF WAY DOWN. (GREASE THE BOTTOM OF THE CUP WITH COOKING SPRAY IF NEEDED, TO HELP WITH STICKING.)
BAKE AT 350 DEGREES FAHRENHEIT FOR 6-7 MINUTES, UNTIL JUST BAKED THROUGH, FOR A SOFT, FUDGY COOKIE. LET COOKIES REST FOR 3 MINUTES BEFORE TRANSFERRING TO A WIRE RACK TO COOL COMPLETELY.
TO MAKE FILLING, BEAT THE BUTTER AND COCONUT OIL/SHORTENING UNTIL SMOOTH IN A LARGE BOWL WITH AN ELECTRIC HAND MIXER. ADD THE POWDERED SUGAR, VANILLA, AND MILK. MIX UNTIL SMOOTH.
PLACE THE FILLING IN A ZIP-TOP PLASTIC BAG AND CUT OFF THE CORNER. PIPE FILLING ONTO THE BOTTOM OF A COOKIE. TOP WITH THE BOTTOM OF ANOTHER COOKIE. REPEAT UNTIL ALL COOKIES ARE PAIRED TOGETHER AND FILLED. STORE LEFTOVER COOKIES IN AN AIRTIGHT CONTAINER OR COVERED WITH PLASTIC WRAP.
