Place water in a cup or small bowl and sprinkle yeast over it. Stir gently and let sit for 5-10 minutes until frothy. This step is for ”proofing” the yeast; if it doesn’t get bubbly, discard and repeat with new yeast.
Meanwhile, in a small saucepan, heat milk just until boiling, then remove from heat and add butter. Mix until butter melts.
In the bowl of a standing mixer (or If you don’t have a mixer, do the whole process by hand), add the lukewarm milk mixture, egg, sugar, and salt. Whisk by hand. Add the water-yeast mixture and mix until combined. Add 3 1/4 cups flour. Fit the mixer with a dough hook and mix on low speed (or by hand with a wooden spoon) for 1-2 minutes, until combined and a dough has formed.
Keep kneading for about 3 minutes on medium-low speed, adding more flour as needed, 1 tablespoon at a time, until the dough feels tacky and moist but does not stick to your hands when pressed. Once it has reached this consistency, keep kneading on medium-low speed in the mixer for another 5 minutes, or by hand on a floured surface for 7-8 minutes, until the dough is elastic and pulls away from the sides of the bowl, yet sticks to the bottom. Don’t be tempted to add a lot of flour – the dough should be slightly sticky, and will be easier to handle after resting. Alternatively, if you feel that the dough is too dry, add a bit water or milk until you reach the desired consistency.
Place dough in a lightly greased bowl and cover with plastic wrap. Let rest in a warm place for 1.5 -2 hours or until dough has doubled in size.
Grease a 10-inch round pan. When the dough has risen, gently punch it to remove air. Divide the dough into 12 equal portions and shape each one into a ball. Place on prepared pan – 9 around the edges and 3 in the middle. There should be gaps between them. Cover and let rest for 45-60 minutes or until again doubled in size.
Preheat oven to 375F/190C.
Brush the rolls with melted butter or an egg wash (egg mixed with 1 tablespoon water) for a shinier look. Bake in the oven for 20 minutes or until the tops have browned and sound hollow when you tap them. A skewer inserted into the rolls should also come out clean. If the rolls brown too fast, cover loosely with aluminum foil. Allow to cool on a wire rack until warm.
Serve warm or at room temperature.
Rolls are best the same day they are made, but can be frozen for up to 2 months.
*Lukewarm water should be around 110F-115F. Any hotter and the yeast will die. If you don’t have a thermometer, then it should feel lukewarm to the touch.