Preheat oven to 425°F. Line a 7-inch cake tin with parchment paper, allowing the paper to extend above the edges.
In a small saucepan over medium-low heat, melt ½ cup sugar until it becomes a deep amber caramel.
Carefully add the cream and stir until smooth. Add a pinch of kosher salt. Let the caramel cool completely.
In a mixing bowl, beat the cream cheese and remaining 3 tablespoon sugar until smooth.
Sift in the flour and mix until no lumps remain.
Add eggs one at a time, mixing fully after each addition.
Stir in the cooled caramel until fully combined.
Pour the batter into the lined cake tin and bake for 30 minutes, or until the top is deeply golden and puffed but the center still jiggles.
Let cool at room temperature for at least 3–4 hours before serving. The center will continue to set as it rests.