Mix the Dough: Add the granulated sugar and egg to the yeast mixture and whisk to combine. Stir in the flour and kosher salt and mix until a shaggy dough forms. Knead by hand or with a dough hook on medium speed for 3 to 5 minutes.

Incorporate the Butter: Add the softened butter one tablespoon at a time, letting each piece fully incorporate before adding the next. Knead for another 5 minutes until the dough is smooth, soft, and just slightly tacky. If it feels really sticky, add flour one tablespoon at a time until it comes together.

First Rise: Transfer the dough to a lightly greased bowl and cover with a clean kitchen towel. Let it rise in a warm, draft-free spot for 1 to 2 hours, or until doubled in size. I like to turn my oven on for 2 minutes, turn it OFF, and then let the dough rise in there.

Make the Custard Filling: While the dough rises, beat the room temperature cream cheese until smooth and fluffy. Add the vanilla extract and heavy cream and mix for 1 minute. Gradually beat in the powdered sugar until the filling is thick, creamy, and lump-free. Transfer to a piping bag or zip-top bag and chill in the refrigerator for at least 30 minutes.

Make the Quick Strawberry Jam (if homemade): Combine 1 cup of diced fresh strawberries with 2 tablespoons of granulated sugar in a small saucepan over medium heat. Cook, stirring occasionally, for 7 to 8 minutes until the berries break down and the mixture thickens slightly. Let cool completely before using.

Make the Lemon Crumble: Stir together the melted butter, flour, granulated sugar, and lemon zest in a small bowl until crumbly. It should hold together when pinched. If it feels too wet, add a little more flour. If it feels too dry, add a small splash of melted butter.

Shape the Buns: Punch down the risen dough and divide it into 6 equal portions. Shape each into a ball, then flatten into a circle about 6 inches in diameter. Place them on a parchment-lined baking sheet with a couple of inches of space between each bun.

Fill the Buns: Brush each dough round with the beaten egg wash. Use the back of a spoon or the bottom of a measuring cup to press a shallow indent into the center of each round. Pipe a generous swirl of the chilled cream cheese custard into each indent.

Add the Strawberry Topping: Spoon a small amount of the strawberry jam over the custard in each bun. Top with the diced fresh strawberries, piling them right into the center.

Add the Crumble: Sprinkle the lemon crumble generously over the top of each bun, making sure to get it around the edges and on top of the fruit.

Bake: Preheat your oven to 375 degrees F. Bake the buns for 20 to 25 minutes, until they are puffed, deeply golden on the edges, and the custard center looks just set and not jiggly.

Cool and Dust: Let the buns rest on the pan for at least 10 minutes before touching them. This allows the custard to fully set. Dust generously with powdered sugar and serve warm.