Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain pasta and transfer to a large bowl. Add the garlic, extra-virgin olive oil, salt, and pepper. Toss to combine.
Meanwhile, warm the olive oil in a medium skillet over medium-high heat. Season the salmon with salt and pepper. Add the fish to the pan and cook until medium-rare, about 2 minutes per side, depending on the thickness of the fish. Remove the salmon from the pan.
Add the basil, capers, lemon zest, and lemon juice to the spaghetti mixture and toss to combine. Set out 4 serving plates or shallow bowls. Place 1/2 cup spinach in each bowl. Top with 1/4 of the pasta. Top each mound of pasta with a piece of salmon. Serve immediately.