Brioche hot cross buns

Name: Brioche hot cross buns
Prep time: 30 min
Cook time: 2 h 30 min
Total time: 3 h
Cuisine: European, Mediterranean, French
Ingredients: 130 g unsalted butter, cut into pieces, plus extra to grease; 200 g milk; 50 g sugar; 2 ½ tsp dried instant yeast; 2 eggs; 500 g baker's flour, plus extra to dust; 1 ½ tsp ground cinnamon; 1 tsp ground nutmeg; ½ tsp ground cloves; 1 tsp sea salt; 250 g mixed dried fruit, of choice (see Tips); 40 g plain flour; 50 g water; 1 tsp extra virgin olive oil; 1 pinch sea salt; 40 g water; 40 g sugar; butter, to serve