Set the oven to 180°C / 350°F, or 160°C fan, and cover 2 baking sheets with parchment paper. The parchment should lie flat beneath the cutouts.
Cream the butter and sugar in a large bowl for 1 minute on speed 5. Look for a creamy mixture rather than an airy, whipped texture.
Beat the egg and vanilla into the butter mixture. Continue until no separate streaks of egg remain.
Put the flour, baking powder, and salt into the bowl. The dry ingredients will sit over the creamy mixture before mixing.
Run the mixer slowly at first, then beat until the flour disappears into the dough. Expect distinct clumps rather than a smooth ball.
Scrape the mixture onto a flour-dusted work surface, press it together, divide it in half, and form 2 discs. Each portion should hold together instead of remaining loose crumbs.
Roll each portion to 0.3cm / 1/8" for crisp cookies or 0.6cm / 1/4" for softer cookies, dusting beneath and above the dough with flour as needed. An even thickness helps the cutouts color consistently.
Stamp out the dough with cookie cutters and lift each shape onto the lined sheets using a knife or spatula, refrigerating dough that must wait for oven space. Support narrow points and branches so they retain their shape during transfer.
Bake for 10 minutes, exchanging the trays’ positions halfway through. Remove them when the tops look pale golden and the edges show their first light golden color.
Leave the cookies on their baking sheets until completely cool. They will continue setting on the warm trays and become firmer as they cool.