Make the filling: In a medium bowl whisk together 1.5 cups creamy peanut butter, 6 tablespoons softened unsalted butter, 2 tablespoons powdered sugar, 2 tablespoons honey, and 1 teaspoon kosher salt until smooth. Cover and chill until ready to assemble.
Prep dry ingredients: In a medium bowl sift together 1.5 cups all-purpose flour, 1 teaspoon baking soda, and 0.5 teaspoon baking powder. Stir in 1 2/3 cups old-fashioned rolled oats and 0.5 teaspoon kosher salt; set aside.
Cream butter and peanut butter: In the bowl of a stand mixer fitted with the paddle (or using a hand mixer), beat 1 cup plus 2 tablespoons softened unsalted butter, 1/3 cup well-mixed chunky natural peanut butter, 3/4 cup sugar, and 2/3 cup packed brown sugar on medium-high until very fluffy and pale, about 3 minutes, scraping the bowl as needed.
Add eggs and vanilla: Reduce speed to medium-low and add the 2 large eggs one at a time, beating to incorporate each, then beat in 1 teaspoon vanilla extract, scraping the bowl as needed.
Combine dough: With the mixer on low, add the dry ingredients in 3 to 4 additions and mix just until combined; do not overmix. Scrape the bowl well to ensure everything is incorporated.
Portion and chill: Using a 1-tablespoon scoop or spoon, portion the dough into 1-tablespoon rounds and place them on a parchment-lined baking sheet. You should have about 70 dough balls. Chill the scooped dough for at least 2 hours.
Bake: Preheat the oven to 375°F (190°C). Arrange up to 12 chilled cookies per baking sheet spaced evenly, then set that sheet inside another baking sheet (double pan). Bake for about 12 minutes, rotating the pan halfway, until evenly golden.
Cool: Remove the baking sheet and cool on a wire rack about 10 minutes before transferring cookies with a metal spatula. Allow cookies to cool completely on the rack; cool baking sheets between batches.
Assemble sandwiches: Place one cookie flat side up, spread about 1 tablespoon chilled filling on it, then top with a second cookie flat side down and press gently. Repeat to make sandwich cookies; make more filling if you prefer fuller sandwiches.