Cook the pasta according to package instructions. Drain and reserve 1 cup of pasta cooking water.
Make the Checca sauce: Combine all the ingredients for the sauce in a food processor and pulse until the tomatoes are crushed. Make sure that the tomatoes are not completely pureed.
Heat 1tbsp olive oil in a saute pan, add asparagus and cook on medium-high heat until they are tender and lightly charred around the edges. Add the spinach and cook until wilted, about 2~3 minutes. Season with salt and pepper.
Add the checca sauce, mix well and turn off the heat.
Stir in the cooked pasta and mix to combine. Add reserved pasta water if the dish looks too dry.