Heat the olive oil in a large Dutch oven over medium heat.
Add the diced onion, carrots, and celery. Cook for 7–8 minutes, stirring occasionally, until the vegetables begin to soften.
Add the garlic, dried sage, thyme, smoked paprika, and nutmeg. Cook for about 30 seconds, stirring constantly, until fragrant.
Add the pumpkin puree and chicken broth. Stir well until the pumpkin is fully incorporated into the broth.
Increase the heat to medium-high and bring the soup to a gentle boil.
Reduce the heat to medium-low and simmer uncovered for 15 minutes, or until the vegetables are tender.
Remove the pot from the heat. Using an immersion blender, carefully blend the soup until smooth and creamy.
Return the Dutch oven to low heat. Add the shredded chicken and milk, then cook for about 5 minutes, stirring occasionally, until the chicken is heated through. Do not allow the soup to boil.
Place the Greek yogurt in a medium bowl. Slowly whisk about ½ cup of the hot soup into the yogurt until smooth. This helps temper the yogurt and prevents it from curdling.
Remove the Dutch oven from the heat and stir the yogurt mixture into the soup.
Add the fresh lemon juice, salt, and black pepper. Stir well, taste, and adjust the seasoning if needed.
Serve warm.