Possible Clues:

• Pungent, edible bulbs
• Skinny enough to get upon NNNNNNNNNN, perhaps
• Tearjerkers, of a sort
• 40A/34D topping
• Spanish rice ingredient
• Knowing these vegetables, you'd be well up
• Shallots' kin
• Bulbs in the kitchen
• Tear-inducing edible bulbs
• What comes on the double is what makes them so skinny