Begin by preheating a large soup pot over medium heat. Add the olive oil and heat until shimmering.
Place the duck breasts, skin side down, into the pot and cook until the skin is golden brown and crisp, about 5-7 minutes. Flip and cook the other side for an additional 5 minutes.
Remove the duck breasts and set aside to rest. In the same pot, add the chopped onion and garlic, cooking until the onion is translucent and fragrant, about 3-4 minutes.
Pour in the chicken broth, scrapping any browned bits off the bottom of the pot with a wooden spoon. These bits add flavor to your soup.
Add the orange zest, fresh orange juice, and thyme to the pot. Bring the mixture to a simmer.
Slice the rested duck breasts into thin strips, ensuring to keep the crispy skin intact.
Add the sliced duck (reserve a few slices for garnish if desired) to the simmering broth and let cook for an additional 10 minutes.
Stir in the heavy cream and continue to simmer the soup until it's heated through, about 5 minutes. Season with salt and pepper to taste.
Serve the soup hot, garnished with fresh parsley, orange slices, and reserved crispy duck slices if desired.