Preheat your oven to 325°F.

Grease a 9-inch springform pan, then wrap the outside tightly with foil for the water bath.

In a small saucepan, melt the 1/2 cup butter over medium heat and cook until it turns golden brown and smells nutty. Remove from heat and cool slightly.

In a bowl, mix the graham cracker crumbs, brown sugar, and browned butter until evenly moist.

Press the mixture firmly into the bottom of the prepared pan and bake for 10 minutes. Set aside while you make the filling.

Beat the softened cream cheese in a large bowl until completely smooth.

Add the granulated sugar and beat until creamy.

Blend in the sour cream, flour, and vanilla.

Add the eggs one at a time, mixing on low speed just until combined. Avoid overmixing.

Pour the filling over the baked crust.

Set the springform pan in a large roasting pan and add 1 to 2 inches of hot water.

Bake for 55 to 65 minutes, until the edges are set and the center jiggles slightly.

Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour.

Remove from the oven and chill for at least 4 hours or overnight.

In a saucepan, melt the remaining 3 tablespoons butter over medium heat and cook until golden and fragrant. Then whisk in the brown sugar, corn syrup, and salt, and cook until the butter is fully blended.

Whisk in the beaten eggs and cook over medium-low heat, stirring constantly, until the mixture thickens, about 5 minutes.

Remove from the heat and stir in the pecans and vanilla.

Allow the topping to cool slightly before pouring it over the chilled cheesecake.

Spread the pecan topping evenly over the cheesecake.

Chill for 30 minutes before slicing and serving.