On a baking sheet, combine the butter, pecans, salt and 1 tablespoon sugar and spread into a single layer. Roast at 350° for 15 minutes. Stir and roast 15 minutes longer. Cool.
For ice cream, in a large saucepan, heat the milk to 175°. Combine sugars and cornstarch; gradually stir into milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Whisk a small amount of the hot 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 the cream , syrup and vanilla. Press waxed paper onto surface of custard. Refrigerate for several hours or overnight.
Stir in the nuts. Place in ice cream freezer and freeze according to manufacturer's directions. Allow to ripen in ice cream freezer or firm up in your refrigerator freezer an hour before serving. Yield: about 2 quarts.