Heat the olive oil in a large non-stick skillet over medium-high heat. Add the gnocchi in a single, even layer (work in batches if necessary to avoid overcrowding). Cook for 3-4 minutes per side, until golden brown, crispy, and pillowy. Use a slotted spoon to transfer the seared gnocchi to a plate and set aside.
Reduce the heat to medium and add the unsalted butter to the same skillet. Once melted, add the minced garlic and optional red pepper flakes. Sauté for about 30-60 seconds until fragrant, being careful not to burn the garlic.
Add the fresh baby spinach to the skillet, working in batches if needed. Stir gently until all the spinach has wilted, which should take about 2-3 minutes.
Pour in the vegetable broth to deglaze the pan, scraping up any delicious browned bits from the bottom with a wooden spoon. Let it simmer for a minute.
Stir in the heavy cream, grated Parmesan cheese, ground nutmeg, salt, and black pepper. Bring the sauce to a gentle simmer and cook for 2-3 minutes, stirring occasionally, until it has slightly thickened.
Return the pan-seared gnocchi to the skillet. Gently toss everything together to coat the gnocchi in the creamy spinach sauce. Let it heat through for about a minute.
Remove the skillet from the heat and stir in the fresh lemon juice. This brightens up all the flavors. Taste and adjust seasoning if necessary. Serve immediately, garnished with extra grated Parmesan cheese.