Place warm milk and yeast in a bowl. Stir to dissolve the yeast in the milk and sprinkle over the sugar to incorporate well. Make sure the milk is warm, not hot, as this can actually damage the yeast. Let the yeast bloom for 5-10 minutes.
In a separate large bowl place flour, salt, melted butter, egg and the yeasty mixture. Mix with a wooden spoon or spatula to combine into a uniform dough.
Use your hands to gently knead the dough. You will know the dough is ready when it doesn't stick to the sides of the bowl anymore.
Add some olive oil in the bowl to prevent sticking, then let your dough prove for 1 hour. The dough will double or even triple in size once proved.
Take out a walnut-sized ball of a ping pong ball and set aside. This will become the teddy bear's ears, nose and eyes.
Divide the rest of the dough into 3 equal parts, which will become the bear heads. Roll each piece into a round ball by folding the edges under themselves, them rolling the dough gently on your work surface.
Place the buns on a lined baking tray, leaving enough distance between the buns.
Divide the ping-pong ball of dough into 3 equal parts for each burger bun. After this, we need to divide the dough into 2 larger balls (for the ears) and 2 smaller balls (for the nose and eyes).
Wet the top of your finger with some water, then gently tap the burger bun where the ears and nose should go. The water will help the dough adhere to itself. Stick on the ears and nose and gently press to secure in place.
The rest of the dough balls remaining from all three buns can be combined so we can colour it. Divide it into two parts and colour one half with red and the other with black food colouring.
Divide the black dough into 9 really small balls of dough. Once more, wet your finger and place small dabs of water where the eyes and nose will go. Place the dough on the water spots you've just made and press gently to fix into place.
The red dough will be divided into 6 small dough balls. Use your fingers to flatten each ball into a disc. Wet the inside of the bear's ears with some water, then place the red disc over it, pressing gently to secure it. We now have ears!
Our bears are now completed, so we need to let them prove for 15-20 minutes. Place a tray or large bowl over the buns, and make sure they don't touch the surface to prevent sticking.
Pre-heat your oven to 180°C (360°F) fan-assisted. While the oven heats, brush the buns with some egg wash, and sprinkle some sesame seeds between the ears - this can become the bear's hair.
Bake the buns for 15 minutes or until golden brown. Once baked, remove from the oven and let cool on a wire rack.
Notes
I recommend using a kitchen scale in grams for more accuracy. The cups used for the conversion are standard US customary cups (1 cup flour = 136g). There are many different types of cups across the globe, which is why I strongly recommend using grams instead.
Storing: you can store any remaining buns in the fridge for up to 2 days, or you can wrap them in cling film and freeze for up to 3-4 weeks.