Add the mini marshmallows and heavy whipping cream to the slow cooker. Sprinkle in 1 tablespoon of the green sanding sugar, reserving the rest for later.
Cover the slow cooker and cook on LOW for 1 1/2 to 2 hours, stirring every 30 minutes. Each time you stir, scrape along the bottom and sides so the marshmallows melt evenly and don’t scorch.
When the marshmallows are fully melted and the mixture looks smooth and pale green, switch the slow cooker to the WARM setting. Using a whisk, beat the mixture briskly for 30 to 60 seconds until it looks slightly thickened, glossy, and fluffy. It should resemble a loose marshmallow cream with a light, airy texture.
Gently fold in the remaining 2 tablespoons of green sanding sugar, stirring just enough to distribute the crystals without fully dissolving them. This keeps the tiny green flecks visible and adds a delicate crunch.
Let the dip stand, uncovered, on the WARM setting for about 5 to 10 minutes to cool slightly and thicken to a scoopable consistency. It will firm up a bit as it sits but should remain soft and dippable.
Serve the shamrock marshmallow dip directly in the slow cooker on WARM, or transfer it to a heatproof serving bowl. Stir occasionally during your gathering to maintain the smooth, fluffy texture. Enjoy with your choice of cookies, fruit, or pretzels for dipping.
For a stronger “shamrock” personality, you can add a few drops of mint extract to the slow cooker during the last 30 minutes of cooking; start with 1/4 teaspoon and taste, as mint can quickly overpower the sweetness. If you prefer a more pronounced green color, stir in a drop or two of green gel food coloring while whisking the melted mixture, but keep it pale so it still looks light and airy. To make individual dessert cups, spoon the warm dip into small ramekins and chill until softly set, then sprinkle each with extra green sanding sugar just before serving. If you’d like a lighter texture, you can whisk the finished mixture vigorously off heat for a few extra minutes to incorporate more air, or briefly beat it with a hand mixer on low right in the slow cooker insert (off the heat) before folding in the remaining sugar. Leftovers can be cooled, covered, and refrigerated for up to 3 days; rewarm gently in the microwave or on LOW in the slow cooker, stirring often, and thin with a splash of cream if it becomes too thick.