Place heavy cream in a medium saucepan, then add seeds from 1 vanilla bean and stir. Bring to a simmer over medium heat, then remove from the heat.
In a separate medium bowl, whisk egg yolks, sugar, and instant espresso powder. Temper the eggs by adding a couple spoonfuls of the warm cream mixture to the bowl, whisking continuously the entire time to ensure the eggs don’t curdle.
Strain the custard through a fine mesh sieve set over a large bowl. Cover tightly, then refrigerate.
Butter or grease a large baking dish. Arrange the croissant pieces. In a large mixing bowl, whisk together heavy cream, whole milk, eggs, egg yolks, melted butter, vanilla extract, ground cinnamon, and a pinch of Kosher salt.
Pour the custard mixture on top of the croissants, then gently stir to ensure they’re evenly submerged. Allow this to sit before baking. When ready, preheat an oven to 350F with a rack set in the center position.
ntil the custard is fully set and the edges of the croissants have crisped up and browned. Cool slightly, then serve warm with chilled crème anglaise drizzled on top.