Stir flour and salt together in the bowl of a stand mixer. Add butter and use the beater attachment to mix until evenly distributed (it should look a bit sandy). If you don't have a stand mixer, you can use a regular electric beater or rub the butter in with your hands.
In a separate smaller bowl, combine boiling water, cold water and milk. Whisk in sugar and yeast. Pour into the flour mixture together with one of the eggs.
Switch to the dough hook attachment and knead until a dough forms and comes away from the side of the bowl (about 8 minutes). It will be a little shaggy and sticky rather than completely smooth. If you don't have a stand mixer you can knead by hand on a lightly floured surface - this can be a bit challenging though given the dough is quite sticky.
Transfer dough to a large, lightly oiled bowl. Cover and place in a warm place to rise until at least doubled in size (approximately 2 hours).
Line a large oven tray with baking paper and lightly dust with flour. Turn dough out onto a lightly floured surface. Weigh and divide into eight equal portions. Gently flatten each piece, gather the ends and pinch the dough to seal in the centre. Flip the dough over (so the smooth side faces up) and roll into a ball.
Use the palm of your hand or a rolling pin to flatten the balls a little (the buns can end up quite tall otherwise, making the burgers tricky to eat!). Place dough on prepared tray, leaving 3-4cm gap between each piece. Cover with lightly oiled cling film and leave on the bench to double in size again (about 1 hour).
Preheat oven to 190ºC fan bake / 210ºC regular bake. Place a metal baking dish on the bottom oven rack. Beat remaining egg together with 1 tablespoon water and use a pastry brush to gently brush over the buns. Sprinkle with sesame seeds.
Place burger buns in the oven and quickly add a cup of water to the metal baking dish below the buns (this creates steam, helping to keep the buns soft). Bake for 18 minutes, until golden brown. Transfer to a wire rack to cool.
These burger buns are delicious fresh on the day they're made, otherwise they can be lightly toasted.
They also freeze really well - perfect for last minute homemade burgers!