In a large heavy saucepan, heat milk and 2/3 cup sugar until bubbles form around sides of pan. Whisk a small amount of hot mixture into 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 spoon.
Remove from the heat. Quickly transfer to a bowl; place in ice water and stir for 2 minutes. Stir in 2 cups cream, cinnamon and vanilla. Press waxed paper onto surface of custard. Refrigerate for several hours or overnight.
For caramel, combine the butter, water and corn syrup in a heavy saucepan. Cook and stir over medium-low heat until butter is melted. Add the remaining sugar; cook and stir until sugar is dissolved.
Bring to a boil over medium heat without stirring. Boil for 4 minutes without stirring. Continue to boil for 12-15 minutes, stirring constantly or until mixture is caramel-colored. Remove from the heat. Carefully stir in remaining cream until smooth; set aside to cool.
Fill cylinder of ice cream freezer two-thirds full; freeze according to the manufacturer's directions. Refrigerate remaining mixture until ready to freeze.
In a large freezer container, layer a third of the ice cream, 1/2 cup caramel, 2/3 cup cinnamon buns and 3 tablespoons pecans. Repeat two times. Swirl mixture; freeze until firm. Serve with remaining caramel. Yield: 2-1/4 quarts.