Step 1 Prepare a grill for medium heat. Toast cumin seeds in a dry small skillet over medium heat, tossing often, until fragrant, about 2 minutes. Let cool.
Step 2 Coarsely crush cumin seeds in a mortar and pestle or with the flat side of a chef’s knife. Transfer to a large bowl. Add lemon juice and honey. Whisk in ¼ cup oil until combined, then stir in chile and ginger—season with salt. Let sit until ready to serve, giving the chile and ginger time to infuse into the sauce.
Step 3 Toss carrots with the remaining 2 Tbsp. of olive oil on a rimmed baking sheet; season with salt. Grill carrots, turning occasionally, until lightly charred in spots and tender, 14–18 minutes. Immediately transfer carrots to bowl with sauce. Toss to coat; season with salt.
Step 4 Arrange avocado and carrots on a platter. Spoon any remaining sauce over, then top with mint. Serve carrots warm or at room temperature.