Anna Olson's Hot Cross Buns

Ingredients

• ¾ cup 2% milk, heated to just above body temperature (105ºF)
• 4 tsp instant dry yeast
• ⅓ cup sugar
• 3 large eggs, at room temperature
• ½ cup vegetable oil
• 3 ¾ cups all-purpose flour
• 1 tsp finely grated lemon zest
• ¾ tsp salt
• ½ tsp ground cinnamon
• ¼ tsp ground allspice
• ¼ tsp ground nutmeg
• ¼ tsp ground clove
• ⅓ cup dried currants
• ¼ cup mixed diced peel
• ½ cup sugar
• 3 Tbsp water
• 1 tsp vanilla extract
• ¾ cup icing sugar, sifted
• 1 Tbsp milk, plus extra if needed