In a heavy saucepan, heat half-and-half to 175°; stir in the brown sugar until dissolved. Whisk a small amount of hot cream mixture into the eggs; return all to the pan, whisking constantly. Cook and stir over low heat until mixture reaches at least 160° and coats the back of a metal spoon.
Remove from the heat. Cool quickly by placing pan in a bowl of ice water; stir for 2 minutes. Stir in whipping cream and vanilla. Press plastic wrap onto the surface of custard. Refrigerate for several hours or overnight. Stir in toasted pecans.
Fill cylinder of ice cream freezer; freeze according to the manufacturer's directions. Allow to ripen in ice cream freezer or firm up in the refrigerator freezer for 2-4 hours before serving.
In a heavy skillet over medium heat, combine pecans, sugar, and butter, stirring constantly for about 6 minutes or until sugar has melted and browned.
Remove from heat; spread nuts on foil.
Once nuts have cooled, break into bite-size pieces and reserve.