Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
Cream together in a large bowl the butter, granulated sugar, and brown sugar until fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, salt, and cardamom.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Gently fold in the chopped peaches.
Drop spoonfuls of dough onto the baking sheet, spacing the dough about 2 inches apart.
In a separate small bowl, mix together the 1 Tbsp cinnamon and 1 Tbsp of sugar. Use a whisk to mix.
Sprinkle each cookie with the cinnamon sugar.
Bake for 12-15 minutes, or until the edges are golden brown.
Remove from the oven and allow cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.
