Preheat your oven to 350°F. Place your pre-baked and cooled 11-inch deep-dish pie crust on a sturdy baking sheet to make moving the filled pie easier.

In a medium mixing bowl, combine the room-temperature cream cheese, granulated white sugar, whole egg plus egg yolk, vanilla extract, and salt. Beat with an electric hand mixer on medium speed for 2 to 3 minutes until the mixture transforms into a completely smooth, velvety, and lump-free batter.

Pour the cream cheese filling directly into the bottom of the cooled pie crust, using an offset spatula to smooth it into a level, uniform layer, then set it aside.

In a small saucepan set over medium heat, whisk together the light corn syrup, packed brown sugar, and 3 tablespoons of all-purpose flour until fully combined. Heat the mixture gently for 1 to 2 minutes just until it warms through and you see a few small bubbles form around the edges; do not bring it to a boil.

Remove the saucepan from the heat source and stir in the melted butter, vanilla extract, and a pinch of salt. Let the warm syrup cool on the counter for 10 minutes.

Slowly stream the cooled syrup into the 4 lightly beaten eggs in a medium bowl, whisking continuously to prevent the warm sugars from scrambling the raw eggs.

Scatter the 1 ½ cups of pecan pieces uniformly across the top of the cream cheese layer in the pie crust. Carefully pour the egg and syrup mixture directly over the pecans; the nuts will naturally rise through the liquid to sit perfectly on top.

Cover the outer edges of the pie crust with a silicone pie shield or a ring of aluminum foil to prevent the pastry from over-browning during the long bake time.

Place the pie on the middle oven rack and bake at 350°F for 1 hour and 10 minutes. Check the pie at the 50-minute mark; if the top pecans look very dark, tent a loose sheet of foil completely over the surface. Remove from the oven the exact moment the outer edges are fully set and the center gives a slight, firm jiggle without looking liquid.

Transfer the pie to a wire rack to cool completely at room temperature, then place it in the refrigerator to chill overnight. This cooling window is essential to allow the hot sugar lipids and cream cheese to firm up into a clean, sliceable state before serving.