Preheat oven to 350°F (180°C).
Cut the butter into chunks and transfer it into a small saucepan. Pour the canola oil into the pan and melt the butter over medium heat.
Crumble the cheese using your hands or a fork. Cutting the cheese into tiny blocks beforehand will make this process easier.
Whisk the eggs, yogurt, salt, and cumin in a glass bowl.
Mix the egg mixture and crumbled cheese until they're evenly combined.
Grease a round baking pan with some of the melted butter.
Place one of the phyllo sheets on your work surface and lightly brush it with some of the butter. Make sure you spread the butter over the entire sheet.
Place another sheet on top, brush it with butter, and spread a handful of the egg and cheese mixture on top. Sprinkle some of the savory on top.
Roll both sheets into a log, then roll the log into a spiral and place it in the middle of the baking pan.
Repeat the same process with the rest of the sheets and roll each log in a circular fashion around the center.
Brush the top of the banitsa with the melted butter until it's completely covered.
Place the pan in the oven and bake for 40 minutes. After you take the banitsa out of the oven, sprinkle its top with some water and cover it with a towel for 15 minutes. This will keep the banitsa moist and prevent it from drying out.
Serve while still warm.