Let’s create this decadent dessert bar, component by component:

1. Prepare Oven and Crust:

• Preheat the oven to 350°F (175°C).
• Line a 9×9 inch baking dish with parchment paper, ensuring there’s an overhang on at least two opposite sides to help lift the bars out later.
• In a medium-sized bowl, combine the graham cracker crumbs, finely chopped pecans, and 3 tablespoons granulated sugar. Stir to mix.
• Add the ½ cup melted (and slightly cooled) salted butter. Stir until all the crumbs are evenly moistened and the mixture resembles wet sand.
• Evenly spread and firmly press the buttered crumb mixture into the bottom of the prepared baking dish.
• Bake the crust for 10 minutes. Remove the baking dish from the oven.
• Lower the oven temperature to 325°F (163°C) for baking the cheesecake.

2. Make the Cheesecake Filling:

• In a small bowl, stir together ¾ cup granulated sugar and 2 tablespoons cornstarch. Set aside.
• In a large mixing bowl (or the bowl of a stand mixer fitted with the paddle attachment), beat the room temperature cream cheese and room temperature sour cream on low speed for 1 to 1½ minutes, until smooth and combined. Scrape down the bowl.
• Keeping the mixer speed on low, gradually add the combined sugar and cornstarch mixture to the cream cheese mixture. Continue mixing on low speed for another 1-1½ minutes, until the sugar mixture is well incorporated and no lumps remain.
• Add the vanilla extract and mix just until incorporated.
• Add the room temperature eggs, one at a time, mixing on low speed just until combined after each egg. Avoid overbeating once eggs are added to prevent cracking. Continue mixing just until a uniform color is reached and no yellow streaks are visible.

3. Bake the Cheesecake Layer:

• Evenly spoon or pour the cheesecake filling over the pre-baked crust. Use an offset spatula to smooth the filling into an even layer.
• Gently tap the baking dish on the counter a few times to release any excess air pockets.
• (Water Bath – Optional but Recommended for Cheesecakes to Prevent Cracking: Though not specified, you can wrap the outside bottom of your 9×9 pan in heavy-duty foil and place it in a larger pan. Pour hot water into the larger pan to come up about 1 inch. This helps with even baking).
• Place the baking dish into the 325°F oven. Bake for 50-55 minutes. The cheesecake is done when the edges are set, but the center will still be slightly wobbly.

4. Cool Cheesecake (Crucial Steps):

• Turn the oven off. Leave the cheesecake inside the closed oven for 30 minutes.
• After 30 minutes, crack the oven door open slightly (prop with a wooden spoon if needed) and let the cheesecake continue to cool in the slowly cooling oven for another 30 minutes.
• Remove the baking dish from the oven and let it sit at room temperature for 1 hour to cool further.
• After cooling at room temperature, cover the pan loosely with plastic wrap and chill the cheesecake thoroughly in the refrigerator for at least 4 hours, or preferably overnight.

5. Make the Pecan Topping (While Cheesecake Chills or After):

• In a small saucepan, melt the ½ cup sliced salted butter and ⅓ cup packed light brown sugar together over medium heat.
• Add the ½ cup dark Karo syrup and ⅓ cup granulated sugar. Bring the mixture to a simmer, stirring occasionally.
• Cook, stirring frequently, for 2 to 3 minutes longer, until the mixture deepens in color slightly and thickens a bit.
• Remove the saucepan from the heat. Carefully stir in the ½ teaspoon vanilla extract and ¼ cup heavy cream. Whisk until smooth. Be cautious as it may bubble.
• Stir in the 1½ cups roughly chopped pecans.
• Let the pecan topping cool for about 15-20 minutes, or until it’s warm but not hot, and has thickened slightly to a spoonable/spreadable consistency.

6. Finish and Serve:

• Once the cheesecake is thoroughly chilled and firm, carefully lift it out of the baking dish using the parchment paper overhang. Place on a cutting board.
• Spoon or pour the slightly cooled pecan topping evenly over the top of the chilled cheesecake.
• Chill for another 30 minutes to 1 hour to allow the topping to set.
• Slice into bars or squares using a hot, sharp knife (wiped clean between cuts). Serve chilled.

This multi-stage process ensures each layer is perfect!