Preheat oven to 400 degrees. Unroll pie crust on a baking sheet and drizzle with butter. Sprinkle with 1 tablespoon brown sugar and cinnamon. Bake for 10 minutes. Cut into strips and let cool.
In a saucepan over medium-low heat, combine the half and half, brown sugar, white sugar, and salt. Stir until sugar dissolves, about 5 minutes.
Take saucepan off heat. Place eggs in a medium bowl. While whisking, gradually (to not curdle the eggs) add about half the sugar/half-and-half mixture to the eggs.
Pour egg mixture into saucepan with the half and half that remained in the saucepan.
Stir in cream.
Cook over medium heat, stirring frequently, until mixture thickens and coats the back of a spoon. About 5 to 10 minutes.
Take saucepan off heat and stir in vanilla extract and almond extract. Pour mixture through a fine-meshed sieve into a bowl and let cool to room temperature.
Place 1 cup of peaches in food processor and process until smooth.
Add processed peaches and chopped peaches to cream mixture.
Pour into an ice cream maker and freeze according to manufacturers directions.
Just before turning ice cream maker off, add about 1/2 the pie crust pieces, crumbling them into the ice cream.
If ice cream is not thick enough for your liking, place in freezer for 1 hour.