Melt butter in a large skillet over medium-high heat.
In a measuring cup or small bowl, whisk together the pineapple juice, brown sugar, cornstarch, and cinnamon until well combined.
Next, add the brown sugar glaze mixture to the skillet with the melted butter. Whisk to combine the reduce the heat to low.
Cook, stirring or whisking occasionally, until thickened, which should take 8 to 10 minutes. Once the glaze mixture is thick, add the tender cooked carrots and pineapple tidbits to the skillet. Use a spatula to stir and coat everything with the glaze. Continue to cook another minute or two until heated through.
Transfer the glazed carrots with pineapple to a serving bowl and serve. This side dish is great with baked ham.