Heat the Dutch oven over medium heat and add oil; sauté the chopped onion until translucent, about 5–7 minutes, then add garlic and cook 1 minute until fragrant.

Add chopped sun-dried tomatoes and tomato paste and cook 1–2 minutes, stirring to caramelize the paste slightly.

Pour in 5 cups chicken stock and bring to a gentle simmer; add the chicken breasts, reduce heat to low, and poach until the internal temperature reaches 165°F, about 12–15 minutes.

Remove the chicken to rest under foil, then use an immersion blender to puree the tomato-onion mixture in the pot until fairly smooth, or transfer to a blender and return the puree to the pot.

Simmer the blended base for 6–8 minutes to concentrate flavor and season lightly with salt and pepper.

Shred or dice the rested chicken and return it to the pot; stir in the heavy cream and bring to a gentle simmer.

Add the potato gnocchi and simmer uncovered, stirring gently, until the gnocchi float and are tender, about 3–4 minutes.

Stir in the baby spinach and cook 30–60 seconds until wilted, then remove from heat and stir in grated Parmesan, basil, and lemon juice if using.

Adjust seasoning with salt and pepper, ladle into bowls, and finish with extra Parmesan and a drizzle of reserved sun-dried tomato oil if desired.