In a bowl take ½ tsp brown sugar and ½ tsp yeast. Add lukewarm water, stir it and let the solution rest until it froths.
In a kneading bowl, take semolina, salt and add activated yeast solution to it. Start binding the dough by adding water little by little.
Once you bind the dough, take it out on the counter for further kneading. Add 1 tbs olive oil in-between. Knead it until it becomes smooth and soft.
Keep the dough in a bowl and let it rest until it becomes double in volume.
Meanwhile, prepare the pesto sauce.
For pesto sauce, in a mixer jar take basil leaves, soaked cashew, garlic cloves, salt, lemon juice, and olive oil. Grind it and your vegan pesto sauce is ready.
Once dough doubles, punch it to release the air. Take the dough out on the lightly floured surface.
Using a rolling pin roll it into a rectangular sheet of 8 x 12 inches and thickness should be ¼ inch.
Spread an even layer of prepared homemade pesto sauce all over the rolled sheet.
Roll the dough sheet tightly starting from the short end just like a roulade.
Using a sharp knife slice the shaped log into two lengthwise.
Then twist the two lengths together and seal both the ends properly.
Place the shaped babka into a 6x3x3 inches greased loaf tin and cover it with cling wrap. Keep the tin in the refrigerator for 8-9 hours.
After 10 hr of resting take the bread tin out from the refrigerator and let it rest on the counter for 10 minutes. Meanwhile, keep the oven for preheating at 200 °C.
Bake the bread in a preheated oven at 200 °C for 30 minutes.
Once baked, take the bread out from the oven and demould it. Let it cool down before slicing.