Melt the butter in a small skillet over medium heat until foamy, nutty, and golden-amber, 3–4 minutes. Add the pecans and toast 1–2 minutes. Strain, keeping the butter and pecans separate. Cool the pecans, then roughly chop.
In a bowl, whisk the whole milk, heavy cream, brown sugar, pudding mix, vanilla, butter extract, salt, and reserved browned butter until the sugar dissolves and the mixture is smooth.
Pour into a Ninja Creami pint below the max-fill line. Cover and freeze flat for 24 hours.
Place the frozen pint in the outer bowl, install in the machine, and run the Ice Cream function.
If the ice cream looks crumbly, run the Re-Spin function once or twice until smooth and creamy.
Make a hole in the center of the pint, add the toasted pecans, and run the Mix-In function.
Scoop and serve, or freeze 1–2 hours for a firmer texture.