Preheat the oven to 325°.
Combine the brown sugar and 5 tablespoons of the granulated sugar in a bowl; set aside.
Spread the bread cubes in a single layer on two rimmed baking sheets. Bake, tossing occasionally, until just dry, about 15 minutes, switching the baking sheets halfway through the baking time. Cool the bread cubes for about 15 minutes.
Pour melted butter over bread and toss to coat. Sprinkle brown sugar mixture over bread and toss to coat. Set aside 2 cups.
Whisk the egg yolks, remaining ¾ cup sugar, vanilla, and salt together in a large bowl. Whisk in the cream and milk until combined. Add the remaining 8 cups bread cubes and blueberries, and toss to coat.
Transfer the mixture to a 9x13 baking dish and let stand, occasionally pressing the bread cubes into the custard, until the cubes are thoroughly saturated, about 30 minutes.
Spread the peaches, cubed cream cheese, and reserved bread cubes evenly over the top of the soaked bread mixture and gently press into the custard.
Place the bread pudding on a rimmed baking sheet and bake on the middle rack until the custard has just set and pressing the center of the pudding with your finger releases no liquid, 45-50 minutes.
Transfer to a wire rack and cool until the pudding is set and just warm, about 45 minutes.
Brush with apricot glaze and serve the bread pudding on top of a few heaping spoonfuls of crème anglaise.