Bring a large pot of salted water to a boil and cook the spaghetti until al dente, about 7 minutes; reserve 1 cup of the pasta cooking water, then drain the pasta.
Heat the extra-virgin olive oil in a small skillet over medium heat until shimmering. Add the sliced garlic and cook, stirring, until golden, about 3 minutes. Transfer the garlic to paper towels with a slotted spoon to drain and crisp.
In a large skillet, heat 1 tablespoon of the oil from the sun-dried tomatoes over medium-high heat. Add the chopped sun-dried tomatoes, washed spinach, and balsamic vinegar.
Cook, stirring, until the spinach is wilted, about 3–4 minutes.
Add the drained spaghetti to the skillet with the tomatoes and spinach. Stir in 1/2 cup of the reserved pasta water to loosen the sauce and toss to combine. Add more pasta water if needed for desired sauciness.
Season with salt and black pepper to taste. Sprinkle the pasta with crumbled feta and top with the toasted garlic chips, then serve warm.
