Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper and set aside.
In a medium bowl, whisk together 2 1/2 cups all-purpose flour (spooned and leveled), 1 1/2 teaspoons baking soda, and 1 teaspoon salt. Set the dry mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup unsalted butter (at room temperature), 1 1/4 cups brown sugar, and 3/4 cup granulated sugar on medium speed until smooth and creamy, about 1 minute. Scrape down the bowl and paddle.
Add 1 cup creamy peanut butter and beat until smooth, about 1 minute. Scrape down the bowl again.
Add 2 large eggs and 2 teaspoons pure vanilla extract and mix until just combined.
Add the dry ingredients to the mixer and mix on low speed until just combined. Do not overmix.
Keep the 2 cups frozen puppy chow frozen until ready to use. If there are any large clumps while still frozen, break them into bite-size pieces. Use a spatula to gently fold the frozen puppy chow and 1 cup chocolate chips into the dough until evenly distributed.
Using a cookie scoop or spoon, portion about 2 tablespoons of dough per cookie. Place scoops onto the prepared baking sheets, spacing them about 2 inches apart.
Bake one sheet at a time (or as space allows) for 11 to 13 minutes, until the edges are golden brown but the centers are still soft.
Remove the baking sheet from the oven. Immediately sprinkle each warm cookie with flaky sea salt, then gently press extra puppy chow onto the tops of the cookies while they are still warm. Lightly dust the cookies with powdered sugar.
Let the cookies cool on the baking sheet for about 5 minutes, or until set. Transfer cookies to a cooling rack and cool completely before serving or storing.