Brown the butter over medium heat, stirring constantly until golden brown. Transfer to a heat-safe bowl, including all browned bits. Cool until room temperature while remaining liquid.
Preheat oven to 350°F. Line a baking sheet with parchment paper.
Whisk together flour, baking soda, baking powder, salt, and cinnamon.
In a large bowl, whisk brown sugar and browned butter.
Mix in egg yolk, corn syrup, vanilla, and blotted sweet potato purée.
Fold dry ingredients into wet ingredients.
Scoop about 3 tbsp of dough and roll in cinnamon sugar.
Place 4–5 cookies on the baking sheet. Top each with 2–3 pecan halves and half of a large marshmallow.
Bake for 11–13 minutes until edges are browned and centers are slightly soft.
If marshmallows slide off, gently move them back with a butter knife sprayed with nonstick spray.
Sprinkle with flaky sea salt.
Cool on a baking sheet for 7–8 minutes before transferring to a wire rack.
Store in an airtight container for 3–4 days.
