In a small skillet, toast pecans in butter for 5–6 minutes or until lightly browned. Cool.
In a heavy saucepan, heat half-and-half to 175 degrees; 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 degrees 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 surface of custard. Refrigerate for several hours or overnight. Stir in toasted pecans.
Fill cylinder of ice cream freezer two-thirds full; freeze according to the manufacturer's directions. Refrigerate remaining mixture until ready to freeze. Allow to ripen in ice cream freezer or firm up in the refrigerator freezer 2–4 hours before serving.
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