There are no known festivals in honour of Hestia in ancient Greece, but her Roman counterpart, Vesta, is honoured during the Vestalia.
The Vestalia took place every year during the ancient Roman calendar between 7 and 15 June. It was one of the most important festivals in the city, mixing both private and public relations. The purpose of this period was to maintain the sacred fire of the city, to provide an opportunity for the matrons to purify themselves, and to offer offerings to guarantee health and prosperity to their homes.
Several Roman authors report that the Cult of Vesta was brought from Alba to Rome by the mother of its founder, Rhea Silvia. According to tradition, it was the son of Romulus, Numus Pompilius who, as a sign of grace to the goddess, established her cult in Rome. The latter has lasted since the origins of Latium, since the last pagan festivities during the emergence of Christianity in 391, when Emperor Theodosius I forbade all religious practices that refer to it.
The festivities took place in 3 stages.
June 7: Opening of the temple
The opening of the Aedes Vestae is exceptional (originally forbidden to everyone except the Vestals and the king or emperor). On that day, the matrons were allowed to go there on pilgrimage. Nevertheless, the rules are strict: they must go barefoot, hair down, in memory of when the temple was surrounded by marshes, and the sjatier of the forum flooded.
June 9: popular festival, religious solemnity
On this day, the Vestal engage in an exclusive meticulous ritual, the preparation of mola salsa, a kind of bread. From the 2nd century BC, trades related to bread and flour, as well as donkeys are honored. The bakers and millers are symbolically related to the bread prepared by the Vestals. As for the donkeys, they have as a symbol their contributions in the mills preparing the sacred flour, but they are also the animal symbol of Priapus and the satyrs. Myths say that when the latter wanted to abuse the sleeping goddess, a donkey brayed, saving her by waking her up. It is in gratitude that processions of donkeys decorated with bread and flowers approach the streets and on the craftsmen exhibit their work as well as their tools and rest.
June 15: Cleansing and closing of the temple
The Vestal Virgins began a ritual of cleansing and purification, called stercoratio. Dirt was evacuated according to a precise ritual. Transported by the way of the clivus capitolinus (Capitoline Hill Climb, an ancient cobbled street in Rome, the main access route to the Capitoline Terrace), to the stercorary gate and then thrown into the Tiber. The operation was also recorded in the official Roman calendars by the formula "Q St D F" Quando stercus delatum fas, meaning, "once the rubbish is removed, the day becomes prosperous".
And here are some ideas for offerings if you want to celebrate it. :
Pule (original cheese served from donkey and goat's milk)
Traditional or contemporary bread (homemade or purchased)
Internal and external purification by water (yourself and your home)
France Minéraux : rites de la Vestalia (a French site)
Nunc est bibendum - Les Vestalia (another french site)
I remind you that English is not my first language, be indulgent if I make mistakes plz I do my best :')