Bananas Foster Bread Pudding

• unsalted butter, to grease and spread
• 20 oz brioche bread, sliced

Lace Cookies

• 2 oz unsalted butter, cubed
• 3 oz light brown sugar
• 2 oz maple sugar
• 2 oz chopped pecans
• 3 tbsp all-purpose flour
• 1 ½ tsp heavy cream
• 1 tsp vanilla extract
• ¼ tsp cinnamon
• 1 pinch salt

Caramel Sauce

• 3 oz unsalted butter
• 5 oz heavy whipping cream
• 4 oz light brown sugar
• 2 oz pure maple syrup
• 1 heaping tsp fine sea salt
• 1 tsp vanilla extract

Egg Mixture

• 6 egg yolks, from large eggs
• 12 oz whole milk
• 3 oz sugar
• 9 bananas, peeled, divided (3 sliced lengthwise (¼ in. thick), 6 halved lengthwise)
• 1 ½ oz unsalted butter
• 2 - 4 oz brandy, to taste
  of 2 - 4 oz bourbon, to taste
• whipped cream, to serve