Peel and dice mangoes into 1-inch chunks. Spread them in a single layer on a parchment-lined baking sheet and freeze for at least 4 hours or until completely solid.
Add the frozen mango chunks to a high-speed blender or food processor. Pour in the honey and lime juice.
Blend on high speed, stopping to scrape down the sides every 30 seconds. The mixture will first look crumbly, then gradually turn creamy and smooth, about 2-3 minutes total. Use the tamper if your blender has one to keep everything moving.
Taste and add more honey if desired, blending briefly to incorporate. The mixture should be thick and scoopable, like soft-serve ice cream.
For soft-serve consistency, serve immediately in chilled bowls. For firmer scoops, transfer to an airtight container and freeze for 2-4 hours.
Before serving frozen sorbet, let it sit at room temperature for 5-7 minutes to soften slightly for easier scooping.