Preheat oven to 375°F (191°C). Line baking sheets with parchment paper or silicone baking mats. Set aside.

In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, beat the butter, brown sugar, and granulated sugar together on medium-high speed until light and creamy, about 3 minutes. Stop and scrape down the sides of the bowl as needed. Add the egg, vanilla, and molasses and beat on high speed until combined, about 1 minute. Scrape down the sides and bottom of the bowl and beat again as needed to combine.

In a medium bowl, whisk the flour, baking soda, salt, cinnamon, cloves, and oats.

With the mixer running on low speed, slowly add the dry ingredients to wet ingredients. The dough will be quite thick and very sticky, and you may have to mix it all by hand after a few seconds in the mixer.

Scoop the dough, about 2 heaping Tablespoons of dough per cookie, and arrange 3 inches apart on the baking sheets. Cookies will spread a bit in the oven.

Bake for 10–13 minutes or until the cookies are very lightly golden around the edges. The centers will look very, very soft.

Remove from the oven and allow the cookies to cool on the baking sheet for 10 minutes before transferring to a cooling rack to cool completely.

For the filling: In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, beat the butter on high speed until creamy, about 1 minute. Add the confectioners’ sugar and beat on medium speed for 1–2 minutes. Pour in heavy cream and vanilla extract. Beat on high speed for 2–3 minutes. Taste and add a pinch or two of salt, if needed. If filling is way too thick, beat in another Tablespoon of room-temperature heavy cream.

Spread about 1.5 Tablespoons of cream filling on the bottom side of half of the cookies; top with remaining cookies, right side up.