In a large skillet over medium heat, melt the butter, then add the pecans and toast, stirring constantly, for 2 to 3 minutes. Sprinkle in the brown sugar and stir until it melts and turns glossy.
Spread the glazed pecans on a baking sheet in a single layer and let them cool completely.
In a chilled bowl, whip the cold heavy cream until stiff peaks form, about 2 to 3 minutes.
In a separate large bowl, whisk together the sweetened condensed milk and vanilla, then gently fold in the whipped cream until no white streaks remain.
Pour half of the mixture into a freezer-safe dish, scatter the cooled pecans evenly over the top, and pour the remaining mixture over them.
Drag a knife through the layers to swirl the pecans throughout.
Cover with plastic wrap and freeze until firm, at least 6 hours or overnight.
Notes
Pull the pecans the moment they smell toasty: They go from toasted to burnt in seconds, and they keep cooking from the pan's heat even after you stop stirring, so take them off early rather than late.Whip to stiff peaks, then stop: Once the cream holds its shape, quit. Keep going and it turns grainy and starts heading toward butter, which won't fold in smoothly.Use fresh pecans: Nuts go rancid, and stale pecans give the whole batch an off, bitter taste. Give them a smell before you toast them.Press plastic wrap onto the surface before freezing: Lay it directly on the ice cream so no air touches it, then store the dish in the back of the freezer where the temperature stays steadiest. Both keep freezer burn and ice crystals away.