Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.

In a large bowl, cream butter, brown sugar, and granulated sugar with a mixer on medium speed until light and fluffy, 2–3 minutes.

Beat in eggs one at a time, then mix in vanilla extract until smooth.

In a separate bowl, whisk together flour, baking soda, salt, and cinnamon. Add the dry ingredients to the wet in two additions, mixing just until combined. Fold in optional crushed toaster pastries and/or white chocolate chips, if using.

Make the filling by stirring together the brown sugar and cinnamon in a small bowl.

Scoop about 2 tablespoons of dough and flatten slightly in your palm. Sprinkle about 1/2 teaspoon of the cinnamon-sugar filling in the center, top with a small pinch of dough, then pinch and roll gently to seal. Place on the prepared sheet, 2 inches apart.

Bake 10–12 minutes, until edges are lightly golden and tops look set but still pale. Cool on the pan for 5 minutes, then transfer to a wire rack to cool completely.

For the drizzle, whisk powdered sugar, 1 tablespoon milk, and vanilla until smooth; add more milk a few drops at a time until it ribbons off the spoon. Add a pinch of cinnamon if desired. Drizzle over cooled cookies and let set before serving.