In a skillet over medium heat, melt 3 tablespoons of butter. Add chopped pecans and cook, stirring occasionally, until toasted, 5 to 8 minutes. Transfer the toasted nuts to a small bowl and let cool completely.

Preheat the oven to 350°F. Grease 3 (9-inch) round cake pans with baking spray and line the bottoms with parchment paper. Wrap with water-soaked fabric baking scrips, if desired.

In a large bowl, whisk together the flour, baking powder, baking soda, and salt.

In a large mixing bowl or the bowl of a stand mixer fitted with a paddle attachment, beat the remaining 1¼ cups butter and granulated sugar together until light and fluffy, 3 to 4 minutes.

Add the eggs, one at a time, beating until combined between each addition. Stop to scrape down sides as needed. Beat in the vanilla.

With the mixer on low speed, add a third of the flour mixture followed but half of the buttermilk. Repeat, alternating between the flour mixture and buttermilk until both are fully combined. Stop to scrape down the bowl occasionally. Fold in the cooled buttered pecans until evenly distributed. Divide the batter among the prepared cake pans.

Bake for 25 to 30 minutes, or until a wooden pick inserted into the center comes out with just a few crumbs. Let the cakes cool for 20 minutes in the pans. Invert onto cooling racks, remove the parchment paper, and let the cakes cool completely.

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter, cream cheese, and salt together on medium speed until creamy and well combined, about 1 minute.

With the mixer on low speed, gradually add the powdered sugar. Stop occasionally and scrape down the bowl. Beat in the cream and vanilla. Once combined, increase the speed to medium-low and beat until smooth and fluffy, about 1 minute.