On a kitchen towel, arrange the eggplant. Season with salt. Let drain for about 10 minutes. Press dry with the towel.
Sift the flour into a medium bowl. Whisk in 1/4 cup oil and 1/2 cup water for the batter.
In another medium bowl, whisk the egg whites until soft peaks form. Fold into the batter.
In a very large skillet, heat about 1/8 inch of oil over medium-low. Add the garlic and rosemary sprigs and cook until aromatic, 2 to 3 minutes. Using a slotted spoon, transfer the garlic and rosemary to paper towels to drain. Increase heat to medium-high.
Stir the chopped rosemary into the batter. Working in 2 batches, dip the eggplant into the batter, then fry in the oil until deep golden and crispy, turning once, 3 to 4 minutes per side per batch. Serve the eggplant hot, drizzled with honey and garnished with the fried rosemary sprigs.