Fresh-Peach Drop Cookies

2 cups all-purpose flour, plus 2 tablespoons
3/4 teaspoon salt
1/2 teaspoon baking soda
1 stick (8 tablespoons) unsalted butter, room temperature
1/2 cup granulated sugar
½ cup brown sugar
1 large egg
1/2 teaspoon pure vanilla extract
2 large ripe peaches, peeled, pitted, and cut into 1/4-inch dice
1/3 cup peach or apricot jam or preserves
2 tablespoons sugar
1/8 teaspoon ground cinnamon

Preheat oven to 375. Whisk together flour, salt, and baking soda.
Beat butter and sugars with a mixer on medium-high speed until light  and fluffy. Reduce speed to low. Beat in egg and vanilla. Mix in flour mixture, and stir until just combined.  Add peaches and jam, and beat until just combined.
Using a 1 1/2-inch ice cream scoop or a tablespoon, drop dough onto baking sheets lined with parchment, spacing about 2 inches apart. (If not baking all of the cookies at once, refrigerate dough between batches; dough can be refrigerated in an airtight container for up to 2 days.) Combine 2T sugar and cinnamon. Sprinkle each cookie with cinnamon-sugar mixture.
Bake cookies, rotating sheets halfway through, until golden brown and just set, 11 to 13 minutes. Let cool on sheets for 5 minutes, and then transfer cookies to wire racks to cool completely.

These cookies are best on the day you bake them!