1. For the Ice Cream: Place the butter in a small saucepan and simmer until the butter turns golden brown. Remove from heat before browning too much and let the butter cool completely.
2. In another larger saucepan, heat the half and half over medium high heat.
3. In a medium bowl, whisk together the yolks, white and brown sugars and salt until smooth.
4. Temper the mixture by adding 1/2 cup of the warmed half and half to the egg mixture and stir together. Add another 1/2 cup of the half and half to the egg mixture and stir together while tempering the egg. Transfer the entire egg mixture into the remaining half and half in the saucepan and stir over medium heat until a thick mixture has formed. The mixture should be 170 degrees F when it's done. Remove the saucepan from the heat and whisk in the seeds from the vanilla bean as well as the browned butter mixture. Let the mixture sit for about 1 hour to infused all the flavor and then strain through a mesh sieve. Discard anything that didn't make it through the mesh sieve and refrigerate the mixture until chilled.
5. Once the mixture is cold, put it into your ice cream maker and churn according to the manufacturers directions.
6. Once fully churned, stir in the streusel and caramelized peaches and freeze for at least 2 hours before serving.
7. For the Caramelized Peaches:Cut the peaches into bite sized pieces and discard the pit. I left the skin on for extra flavor and color. Place the peaches into a sauce pan with the lemon juice and white sugar. Heat the sauce pan over medium heat until the peaches start to cook. Cook the peaches for about 10 minutes, stirring frequently and then remove from the heat and set aside to cool.
8. For Cinnamon Streusel:Preheat the oven to 350 degrees F.
9. In a food processor, combine the flour, butter, sugar and cinnamon and pulse for a few seconds to break up the butter. Place the mixture on a parchment lined baking sheet and bake for 7-10 minutes.
10. Remove the streusel from the oven and let cool. Once cooled, break it into bite sized pieces if needed and use as needed.
FOR SUGAR COOKIES:
1. Preheat your oven to 350 degrees F.
2. Cream together the butter and sugars in a mixer. Add the eggs and vanilla, making sure to scrape down the sides of the mixing bowl. Add the flour, salt, baking soda and baking powder and mix on low until everything is incorporated.
3. Chill the dough in the refrigerate for 2 hours. Scoop out some dough, and roll it into a ball. It should be about the size of a golf ball.
4. Place the cookie on a parchment lined baking sheet. Place 6 cookies on a sheet since they will spread due to their size.
5. Bake for 14-15 minutes until just slightly golden around the edges. Remove from oven and let rest on the baking sheet. If you want to flatten them out a big, carefully bang the baking sheet on the counter to release any excess air in the cookies. Note They might look a little under baked in the middle - but don't fear!! They will continue to bake a bit once removed from the oven.