Preheat oven to 350°F (180°C). Line a baking sheet with parchment paper and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with an electric mixer, cream the butter, light brown sugar, and granulated sugar together on medium-high speed until light and creamy, about 2 minutes. Add in the eggs and the vanilla and mix until combined, scraping down the sides as needed. Set aside.
In a medium bowl, whisk the flour, baking soda, salt, cinnamon, cloves, and oats together. With the mixer on low, slowly add the oat mixture to the wet ingredients, mixing until just combined. (The dough will be thick).
Using a large cookie scoop, scoop the dough onto the prepared baking sheet, leaving about 2.5 inches between each cookie (they will spread as they bake). Bake for 12-14 minutes, or until lightly golden brown around the edges. Allow cookies to sit on the pan for about 3 minutes before removing them to a wire rack to cool completely. While the cookies cool, prepare the crème filling.
To Make the Vanilla Bean Creme Filling:
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with an electric mixer, beat the butter on medium-high speed until fluffy and lighter in color, about 5 minutes.
Turn the speed down to low and gradually add in the powdered sugar. Continue mixing on low speed until the powdered sugar is completely incorporated. Add in the vanilla bean paste and heavy cream and mix until combined.
Turn the mixer back up to medium-high speed and beat the mixture for an additional 3-5 minutes until the buttercream is fluffy. If needed, add in a little more cream 1 teaspoon at a time until you reach your desired consistency.
To fill and assemble, pipe or spread about 1½ tablespoons of creme filling on the bottom side of half of the cookies; top with the remaining cookies, right side up.
The oatmeal creme pies will stay fresh and soft at room temperature for 2 days in an airtight container. Alternatively, store in an airtight container in the refrigerator for up to 4 days.