1. Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the cubed chicken and cook, stirring occasionally, until it’s lightly browned on all sides and mostly cooked through, about 5-7 minutes. The chicken should no longer be pink on the outside. Remove the chicken from the pot and set it aside on a plate.

2. Reduce the heat to medium. Add the sliced leeks to the same pot, adding a splash more olive oil if needed. Saute the leeks for about 5-7 minutes, stirring frequently, until they are softened and translucent. They should look wilted and slightly sweet-smelling.

3. Stir in the minced garlic and dried thyme. Cook for another minute until the garlic is fragrant, being careful not to burn it. The kitchen will start to smell wonderfully aromatic at this point.

4. Pour in the chicken broth, scraping the bottom of the pot with a wooden spoon to loosen any browned bits. These bits add a lot of flavor to the soup. Bring the broth to a gentle simmer.

5. Add the cooked chicken back into the pot. Stir in the heavy cream, salt, and black pepper. Continue to simmer gently for about 5 minutes, allowing the flavors to meld and the soup to heat through completely. The soup should be lightly bubbling, not boiling vigorously.

6. Finally, add the fresh spinach or mixed greens to the pot. Stir until the greens have wilted, which usually takes only 1-2 minutes. The vibrant green color will pop against the creamy broth. Taste and adjust seasonings as needed. Serve hot.