Dissolve the yeast in the warm water (be sure the water isn't too hot as that could kill the yeast). Leave for 5-7 minutes until the mixture starts to bubble.
Mix the dry ingredients together in a large bowl (use a mixer bowl if you have one). If mixing by hand, make a well in the centre of the dry ingredients.
Add the yeast mixture to the dry ingredients. If using a mixer, use the dough hook attachment and knead at a medium speed for 5-10 minutes. Otherwise, knead by hand until a soft, stretchy dough forms. It should be easy to handle.
Oil a large bowl and put the dough inside. Cover with a clean tea towel and leave for around 90 minutes to proof. The dough should double in size.
Preheat the oven to 200°C fan bake.
Dissolve the sugar in a bowl of hot water. Place the sesame seeds in a second bowl.
Divide the dough into 10 equal portions (roughly around 80g each). Use your hands to roll the dough into long, thin, sausage-like shapes. Join the ends together with olive oil to form a hoop (you can twist the dough before joining the ends if you like).
Dip each hoop into the syrup mixture, then coat in sesame seeds. Then place on a baking tray. You should be able to fit five koulouri on a standard baking tray, depending how large you make them.
Bake for 15-20 minutes. If you want a very crispy crust, pour a cupful of water into a baking pan at the bottom of the oven after you put them in.
Brush with melted butter while they're still warm. Serve with feta cheese and tomatoes.