Step 1

Place a rack in center of oven; preheat to 325°. Butter a 2-qt. baking dish. Cut each doughnut into eighths and arrange on a parchment-lined rimmed baking sheet. Bake until dry and crisp, like little sugary croutons, about 15 minutes. Let sit until cool enough to handle. (Drying out the doughnut pieces will help them absorb the custard.)

Step 2

Vigorously whisk eggs, egg yolks, half-and-half, sugar, vanilla, salt, and lemon zest in a large bowl until light, uniform, and foamy. (You can also process in a blender until combined if you want.) Add doughnuts to bowl with custard. Gently toss and push down on them so that they absorb maximum liquid without falling apart. Let sit 5 minutes, then toss and press gently again. Repeat tossing and soaking twice more for a total soak time of 15 minutes, allowing the doughnuts to fully drink up the custard.

Step 3

Transfer doughnuts and any remaining custard to prepared baking dish. Dollop preserves over, avoiding edges of pan where it can burn during baking. Bake bread pudding, rotating pan halfway through, until puffed, golden brown, and bubbling along the edges, 50–60 minutes.

Step 4

Let bread pudding cool 20 minutes. Dust with powdered sugar. Serve with cream alongside for pouring over.

Step 5

Do Ahead: Doughnuts can be baked 1 day ahead. Store in an airtight container at room temperature.