Possible Clues:

• Peppery root
• Red salad veggie
• Very handsome artist in salad
• Vegetable with a variety called French Breakfast
• A ruddy vegetable meal for the artist
• Salad vegetable in a meal linked to recipe
• Salad plant artist's shown on plate
• Is unusually hard on the outside, but edible
• Possible follower of horse god having meal
• Sounds as if one might take it as read that that's something for the Academician to eat