Grease a 9x13-inch baking pan with butter.

In a large mixing bowl, combine the bread cubes and quartered strawberries. Toss together gently with hands, taking care to not crush the cubes; set aside.

In a medium mixing bowl, whisk together the milk, cream, eggs, sugar, cornstarch, vanilla, cinnamon, salt, and lemon zest until smooth and evenly blended.

Pour the milk mixture over the bread cubes and gently toss with a rubber spatula to coat the bread.

Transfer the bread mixture into the prepared baking pan. Make sure mixture is spread evenly in pan.

Cover pan with plastic wrap or foil and let rest at room temperature for 1 hour.

While the bread pudding is resting, make the strawberry purée. Place the whole strawberries in a food processor or blender.

Blend until smooth, then pour the purée through a fine mesh strainer into a measuring cup or bowl, straining out the seeds. Cover and refrigerate until ready to use.

Preheat oven to 350º F.

Once the bread pudding has rested for an hour, remove the plastic or foil, place the pan on a rimmed baking sheet to catch any drips, and bake uncovered for 60 to 70 minutes until bubbly and golden.

Test for doneness by inserting a butter knife into the center of the pudding and moving it slightly to create a small hole. If the hole collapses and fills with watery liquid the pudding is not done yet. If the hole stays open and no liquid is visible, it is finished cooking.

Remove from oven and let cool for 10 minutes.

Serve warm with a drizzle of strawberry purée and a scoop of vanilla ice cream, if desired.