Dice the onion, carrots, celery, potato, and pumpkin into uniform bite-sized pieces.
In a large pot, heat 0.25 cup of the vegetable broth over medium heat and sauté the onion, carrots, and celery until the onion is translucent.
Stir in the potato, pumpkin, and the remaining vegetable broth, then bring the mixture to a gentle boil.
Reduce the heat to low, cover, and simmer for 20 minutes or until the potatoes and pumpkin are fork-tender.
Stir in the cannellini beans, sea salt, black pepper, and fresh thyme, allowing the soup to heat through for 5 minutes.
Carefully crack the three eggs into the simmering broth one at a time, spacing them apart, and cover the pot for 3-4 minutes until the whites are set but the yolks remain soft.
Ladle the broth and vegetables into bowls, gently placing one poached egg on top of each serving.