Cut the vegetables into sticks of about the same size. Place on a baking sheet lined with parchment paper, sprinkle with salt, a few tablespoons of oil, and thyme leaves, and bake in a preheated oven at 180 °C for about twenty minutes (they should not be too charred).
In the meantime, beat the eggs, milk and oil in a bowl, add the flour and baking powder, sifting them a little at a time, and mix with a wooden spoon.
Add the cheese. Remove the vegetables from the oven and let them cool; then mix them with the Amarena Fabbri cherries, whole or cut to taste, and then add everything to the mixture.
Pour into a buttered and floured mold and return to the oven for about 50 minutes.