Start by boiling some water and adding your pasta shells once it is bubbling away. You will know they are ready when they are tender but still firm to the bite. Just be careful not to overcook them or they might get mushy and will not hold the sauce well.
Heat olive oil in a pan, and toss in the minced garlic. Let it sizzle for a minute until it is fragrant and golden. Then add the green pesto, mixing it until it is well blended with the garlic.
Pour in the white wine and allow it to simmer. You will notice the lovely aroma merging with the pesto. This step helps lift the flavors, but it is easy to let it cook too long; just a few minutes is all it needs.
Now, add the heavy cream and stir gently. The sauce should start to thicken while becoming creamy and luscious. Do not leave it unattended, as it can curdle if it gets too hot.
Squeeze in fresh lemon juice, giving it a nice zing. This adds a delightful brightness to the sauce, cutting through the richness. If you find it too tangy, you can always add a bit more cream to balance things out.
Toss in the mozzarella and stir until it is melted and gooey. You will want it to blend smoothly into the sauce, forming a delicious texture.
Season with salt and pepper to taste. Give the sauce a final stir to meld everything together. Avoid adding too much salt at once; you can always add more if needed.
Add the cooked pasta shells to the sauce, gently folding them in until they are coated evenly. Be mindful not to break the shells while mixing.