Using a food processor, puree the spinach, almonds, garlic and 1 tbsp. lemon juice. With the machine on, gradually pour in 1/3 cup EVOO until smooth. Pulse in 1/2 cup parmesan; season with salt and pepper. Taste and add more lemon juice if desired.
In a large skillet, heat the remaining 1 1/2 tbsp. EVOO over medium-high heat. Add the gnocchi in a single layer and cook, undisturbed, until golden and crisp, 3 to 4 minutes; turn and cook, tossing occasionally, until golden all over, about 2 minutes. Stir in the tomatoes and cook until heated through, about 2 minutes. Remove from the heat and stir in the pesto. Top with the goat cheese.