Preheat the oven to 325°F (160°C). Lightly butter or spray a 12-cup muffin tin and line each cup with a paper liner or silicon liner if desired.

Make the sponge base: whisk together 3/4 cup all-purpose flour (95 g), 1/2 cup granulated sugar (100 g), 1 teaspoon baking powder, and 1/4 teaspoon salt in a medium bowl.

In a separate bowl, whisk the large egg, 1/3 cup melted cooled unsalted butter (75 g), and 2 tablespoons whole milk until combined. Add the wet ingredients to the dry mix and stir until just combined; do not overmix.

Spoon about one heaping tablespoon of the batter into each prepared muffin cup, forming a thin sponge layer. Reserve the remainder for any cups that need topping. Bake the sponge layers for 6–8 minutes until just set but not browned. Remove from oven and let cool slightly.

Reduce oven temperature to 300°F (150°C). Prepare a large baking dish for a water bath by placing a folded kitchen towel on the bottom (optional) and positioning it so it will support the muffin tin flatly.

Prepare the cheesecake filling: in a mixing bowl, beat 8 ounces cream cheese (225 g) with 1/2 cup granulated sugar (100 g) on medium speed until smooth and free of lumps, scraping the bowl down halfway through.

Add 2 large eggs, one at a time, mixing on low speed until just combined after each addition. Scrape down the bowl so the mixture is even.

Warm and add the dairy: very gently heat 1/2 cup heavy cream (120 ml) just until it loses chill but does not boil; let it cool slightly. Stir in 1/4 cup sour cream (60 g) and the seeds from 1 vanilla bean or 2 teaspoons vanilla extract, mixing until smooth.

Add 1 tablespoon all-purpose flour and a pinch of fine salt to the filling and fold gently to incorporate. The batter should be silky and pourable without lumps.

Pour the cheesecake filling on top of the partially baked sponge layers, filling each muffin cup nearly to the rim but leaving a small gap to prevent overflow. Tap the tin gently on the counter to release any trapped air bubbles.

Place the filled muffin tin into the prepared baking dish, then pour very hot water into the baking dish until it reaches halfway up the sides of the muffin tin to create a bain-marie (water bath). Be careful not to splash water into the cups.

Bake at 300°F (150°C) for 20–25 minutes. The centers should be set but still slightly jiggly when the pan is nudged. Avoid overbaking for the creamiest texture.

Turn off the oven and prop the door open slightly; allow the tin to cool in the oven for 30 minutes to reduce shock and prevent cracking, then remove and cool to room temperature on a rack.

Once cooled, transfer the cupcakes to the refrigerator and chill for at least 4 hours, preferably overnight, to allow the cheesecake filling to fully set.

When ready to finish, pat the tops of each chilled cupcake dry with a paper towel. Sprinkle about 1/2 to 1 teaspoon granulated sugar evenly over each top to form a thin layer for caramelizing. For a more dramatic crack, use coarse sanding sugar or a mix of fine and coarse sugar.

Caramelize the sugar using a butane kitchen torch: hold the flame about 2–3 inches from the sugar and move it in a slow circular motion until the sugar melts, bubbles, and turns a deep amber. Allow the caramel to harden for a minute before serving.

If you don’t have a torch, preheat the oven broiler on high and position the top oven rack about 6 inches from the broiler element. Place the cupcakes on a baking sheet and broil for 1–3 minutes, watching constantly, until the sugar melts and caramelizes; remove immediately to cool and harden.

If desired, add a small flake of coarse sugar or a shard of torched sugar as garnish for texture contrast and visual appeal. Serve chilled or bring to room temperature for 10–15 minutes before eating for a softer mouthfeel.