Short Story collection read in 1990s/2000s about man riding giant rooster

[Christina]

I read a book in childhood (1990s/2000s). It was a short story collection. One story stuck out to me. A man was riding a giant rooster that was wounded. He placed a seed on the wound and a palm tree grew. Another story involved a frog.

[Becca]

South and North, East and West: The Oxfam Book of Children's Stories by Michael Rosen? It has a story called 'A Story for a Princess', which sounds like what you remember:

[the egg] fell out of my hands and fell, splat, onto the ground. And it broke open and out stepped a giant rooster.
"Get on my back and I'll carry you home!" it said to me.
[...]
As I bent down to have a closer look, my foot knocked against the rooster's neck and right away a big hole appeared in the skin, and blood started pouring out. But the rooster didn't seem to mind at all.
"Take a date out of your pouch," he said. "Eat it and keep the stone. The stone will turn to powder. Rub the powder into my wound."
So I did as he told me and after I rubbed the powder in, a palm tree started to grow out of the hole.

The book describes this as a traditional story / folk tale from the Middle East, so it might appear in other books as well, but fingers crossed this is the one!