Parashurama, having given the whole earth away, stands on the Western Ghats and throws his axe into the ocean; Varuna draws the water back as far as it flew, and the coast from Gokarna to Kanyakumari rises, which he settles with brahmins brought from the north.
The Kerala chronicle begins with the axe. Parashurama, his killing done and the earth given away, stands on the Sahyadri, the Western Ghats, faces the ocean, and throws his axe as far as he can. The waters go back to where it falls and a long strip of land comes up between the mountains and the waves, from Gokarna to Kanyakumari. He brings brahmins from the north and settles them in sixty-four villages, thirty-two of them in Kerala. They are frightened of the serpents who already live there and go home; he fetches a second group, and changes their hair and dress so that the north will not take them back. He founds a hundred and eight temples and gives the land its rites.
South India · Gokarna and the western coastAll traditions
In the Brahmanda Purana's telling the land was there before and the sea took it. When Ganga came down to earth her flood ran to the western sea and drowned the holy place of Gokarna. Its hermits climbed to Mahendra and told Parashurama. He went to the shore and called on Varuna, who did not come; he stood in meditation until his weapons came into his hands, and Varuna came in fear and agreed to give the land back. Parashurama sent the weapons away and threw a winnowing basket, a shurpa, over the water, and the sea retreated to where it fell. The land is called Shurparaka. The Mahabharata has a third reason: Kashyapa, given the earth, asked its giver to leave it, so he shot an arrow into the sea and made land for himself.
Sources: Keralolpathi (Wikipedia); Parashurama and the coast that rose from the sea (Say Solmelu); Story of Kerala, in Vettam Mani's Puranic Encyclopaedia (wisdomlib)