Cheesy garlic bread babka

Name: Cheesy garlic bread babka
Cook time: 1 h 20 min
Total time: 1 h 20 min
Cuisine: European, Eastern European
Ingredients: 100ml whole milk; 275g strong white bread flour plus extra for dusting, optional; ¼ tsp cayenne pepper; 1 tbsp caster sugar; 1 tsp fast-action dried yeast; 2 medium eggs at room temperature; 75g unsalted butter at room temperature, cut into cubes; 75g unsalted butter softened; 3 cloves garlic crushed; a handful flat-leaf parsley finely chopped; 75g cheddar grated; 75g mozzarella from a block finely chopped