Prepare the Brioche Dough: In a mixing bowl, combine warm water with sugar and active dry yeast. Let sit for about 5 minutes. In a stand mixer, combine flour and salt, then incorporate the yeast mixture and eggs. Gradually add softened butter and mix until smooth and elastic.

Knead and Let the Dough Rise: Knead the dough on a floured surface for 5 minutes. Shape it into a ball, oil lightly, and place in a bowl covered with a damp cloth. Let rise for about 1 hour or until doubled in size.

Make the Peach Filling: In a saucepan, melt butter and add diced peaches. Cook with peach nectar for 5-7 minutes. In a bowl, mix cornstarch, cinnamon, and salt; add to peaches, stir, and boil until thickened. Cool the mixture and refrigerate overnight.

Prepare the Crisp Topping: Preheat the oven to 350°F. Mix brown sugar, oats, flour, and spices in a bowl. Stir in melted butter. Spread on a baking sheet and bake for 15-20 minutes until golden brown. Let cool.

Shape and Fry the Doughnuts: Roll out dough to 1/4 inch thickness and cut out circles. Let them rise for another 30 minutes. Heat oil to 340-350°F. Fry doughnuts until golden brown, about 2-3 minutes per side.

Fill and Top the Doughnuts: Once cooled, fill each doughnut with peach filling using a pastry bag. Mix icing sugar with peach nectar and butter. Drizzle over filled doughnuts and top with crisp topping. Serve warm.