Line a baking sheet with a silicone baking mat or parchment paper.
Have a biscuit cutter, or a tall cookie cutter between 1 and 2 inches in diameter, ready.
Put 1/2 Tablespoon butter in a small skillet or saucepan and cut the remaining butter into 12 pieces.
Set the pan over low heat, melt the butter, and add the onion.
Cook, stirring, just until onion softens, about 3 minutes; take pan off heat and set aside.
Put the flour, baking powder, sugar, and salt in a bowl; whisk to combine.
Drop the butter pieces into the bowl and, using your fingers, rub the butter into the flour mixture until you've got a bowl full of flour-covered pieces, some small and flaky, some the size of peas.
Scatter the cooked onion over the mixture.
Pour over the cold milk and, using a fork, toss and turn everything together until you've got a soft dough.
If there are some dry bits at the bottom of the bowl, reach in and knead the dough gently a couple of times.
Lightly dust a work surface with flour, turn the dough out, and dust the top of the dough very lightly with flour.
Pat the dough down gently with your hand (or roll it out with a rolling pin) until it is about 1/2 inch thick. It doesn't have to be an even square or round; just do the best you can, and do it quickly.
Dip the biscuit cutter into the flour bin and cut out as many biscuits as you can (cutting the biscuits as close to one another as possible).
Transfer viscuits to the baking sheet, leaving a little space between them.
Gather the scraps of dough together, pat them down, and cut out as many more biscuits as you can; put these on the lined baking sheet too.
Alternately, you can pat or roll out the dough into a rectangle or square, the, using a long knife, cut square biscuits, about 1 to 1-1/2 inches on a side.
You can make the biscuits to this point and freeze them on the baking sheet. When they are frozen solid, pack them airtight and freeze them for up to two months.
Bake the biscuits for 15 to 18 minutes or until they are puffed and lightly browned. Add a couple more minutes if biscuits are frozen.
They are ready to eat now or to use to make cocktail sandwiches.