In a large, heavy-bottomed saucepan, combine the chopped rhubarb, granulated sugar, water, ground cinnamon (if using), and ground ginger (if using). Stir gently to combine.

Bring the mixture to a simmer over medium heat, stirring occasionally. Once simmering, reduce the heat to low and continue to cook, stirring frequently, for 20-25 minutes, or until the rhubarb has completely broken down and the mixture has thickened considerably.

Remove the saucepan from the heat. For a smooth rhubarb butter, carefully transfer the mixture to a food processor or use an immersion blender to purée until smooth. If you prefer a slightly chunkier texture, you can mash it with a potato masher.

Return the puréed rhubarb mixture to the saucepan over low heat. Add the cold, cubed unsalted butter and stir constantly until the butter has fully melted and incorporated into the rhubarb mixture, making it glossy and smooth.

Cook for another 5 minutes, stirring, allowing the butter to emulsify and the mixture to thicken further. Be careful not to boil it once the butter is added.

Remove from heat and let it cool slightly. Transfer the Rhubarb Butter to clean, airtight jars. It will continue to thicken as it cools. Store in the refrigerator for up to 2-3 weeks.