Heat 1 tablespoon of the reserved sun-dried tomato oil in a large deep skillet (cast iron or stainless steel) over medium heat.
Add the diced shallot and sliced sun-dried tomatoes. Sauté for 2 minutes until fragrant and softened. Stir in the minced garlic, Italian seasoning, and red pepper flakes, cooking for 30 seconds until aromatic.
Pour in the broth and heavy cream, whisking gently to combine. Season with sea salt and freshly cracked black pepper. Bring the liquid to a gentle simmer over medium heat.
Add the uncooked potato gnocchi directly into the simmering cream sauce. Stir gently so gnocchi are submerged. Cover the skillet with a lid and cook for 4 to 5 minutes, stirring occasionally, until the gnocchi are plump, pillowy, and tender.
Remove the lid and reduce heat to low. Stir in the fresh baby spinach in handfuls until wilted into the sauce (about 1 minute).
Scatter the shredded fontina and grated Parmigiano-Reggiano into the skillet. Gently fold until the cheese melts into a glossy, velvety blush sauce that clings to every dumpling.
Remove from heat, garnish generously with fresh torn basil and shaved parmesan curls, and serve immediately with warm crusty garlic bread.