Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper or silicone baking mats.

In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes. You can use an electric mixer for best results.

Beat in the egg and vanilla extract until well combined, scraping down the sides of the bowl as needed.

In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.

Gently fold in the finely diced rhubarb. The mixture will be thick.

Drop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between each cookie.

Bake for 10-12 minutes, or until the edges are lightly golden and the centers are just set. Do not overbake. Let cookies cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.

If desired, prepare the glaze: In a small bowl, whisk together the powdered sugar and milk/lemon juice until smooth and pourable. Drizzle over cooled cookies and allow glaze to set before serving.