Step 1: Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats.
Step 2: In a large bowl, cream together the 1 cup softened unsalted butter and 1 ½ cups brown sugar until light and fluffy. Use an electric mixer for best results.
Step 3: Beat in the large egg and 1 tsp vanilla extract until well combined.
Step 4: In a separate medium bowl, whisk together the 2 ½ cups all-purpose flour, 1 tsp baking soda, and ½ tsp salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Step 6: Gently fold in the 1 ½ cups finely diced rhubarb until evenly distributed throughout the dough.
Step 7: Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Step 8: Bake for 12-15 minutes, or until the edges are lightly golden and the centers are set. Do not overbake to keep them soft.
Step 9: Remove cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Step 10: While cookies are cooling, prepare the cream cheese frosting. In a medium bowl, beat the 4 oz softened cream cheese and ½ cup softened unsalted butter until smooth and creamy.
Step 11: Gradually add the 2 cups powdered sugar, beating until fully incorporated. Add 1 tsp vanilla extract and beat until light and fluffy.
Step 12: If the frosting is too thick, add milk or cream one tablespoon at a time until desired consistency is reached.
Step 13: Once the cookies are completely cool, spread or pipe the cream cheese frosting generously onto each cookie.
Step 14: Serve immediately or store in an airtight container in the refrigerator.