Step 1: Make the Custard Filling

1. Heat the Cream and Milk: In a medium saucepan, combine 1 cup heavy cream and 1/2 cup whole milk. Heat over medium heat until small bubbles start to form around the edges, but do not let it boil.
2. Whisk the Egg Yolks and Sugar: In a mixing bowl, whisk together 4 egg yolks, 1/3 cup granulated sugar, vanilla extract, and a pinch of salt until smooth and slightly pale.
3. Temper the Egg Mixture: Slowly pour about half of the warm cream mixture into the egg yolks while whisking constantly. This process, known as tempering, prevents the eggs from scrambling. Once combined, pour the egg mixture back into the saucepan with the remaining cream.
4. Cook the Custard: Stir the custard mixture over medium-low heat until it thickens enough to coat the back of a spoon, about 5-7 minutes. Do not let it boil. Once thickened, remove from heat.
5. Strain and Chill: Pour the custard through a fine-mesh sieve into a clean bowl to remove any small lumps. Cover with plastic wrap, pressing the wrap directly against the surface of the custard to prevent a skin from forming. Chill in the refrigerator for at least 1 hour or until fully set.

Step 2: Make the Vanilla Cupcakes

1. Preheat the Oven: Preheat your oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.
2. Mix the Wet Ingredients: In a large bowl, beat together the softened butter, vegetable oil, and granulated sugar until light and fluffy. Add the egg and vanilla extract, and beat until smooth.
3. Add the Dry Ingredients: In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, alternating with the milk. Begin and end with the dry ingredients, mixing just until combined. Be careful not to overmix, as this can result in dense cupcakes.
4. Fill the Cupcake Liners: Divide the batter evenly among the cupcake liners, filling each about 2/3 full.
5. Bake the Cupcakes: Bake for 18-20 minutes, or until a toothpick inserted into the center of a cupcake comes out clean. Remove from the oven and allow the cupcakes to cool completely on a wire rack.

Step 3: Fill the Cupcakes with Custard

1. Core the Cupcakes: Once the cupcakes have cooled, use a small knife or cupcake corer to create a hole in the center of each cupcake. Remove a small portion of the center, creating a space for the custard filling.
2. Fill with Custard: Spoon the chilled custard filling into each cupcake, filling the hole to the top. You can use a piping bag for easier filling if you prefer.

Step 4: Make the Caramelized Sugar Topping

1. Sprinkle Sugar on Each Cupcake: Sprinkle about 1 teaspoon of granulated sugar evenly over the top of each filled cupcake.
2. Caramelize the Sugar: Using a kitchen torch, carefully heat the sugar on top of each cupcake until it melts and turns a golden brown color, forming a crisp layer. Be cautious and avoid holding the torch too close to the sugar to prevent burning.
3. Let Cool: Allow the caramelized sugar to cool and harden for a minute or two before serving. The top should be crisp and crack when you bite into it, just like traditional crème brûlée.