Preheat oven to 350°F (175°C) and spray a 9×13-inch baking dish with cooking spray.
Bring a large pot of lightly salted water to a boil.
Add lasagna noodles and cook for 8–10 minutes until al dente.
Drain noodles and set aside.
Spray a large skillet with cooking spray and heat over medium-high.
Sauté onion and garlic for 3 minutes until onion is tender-crisp.
Stir in vegetable broth and rosemary and bring to a boil.
Add artichoke hearts and spinach and reduce heat to low.
Cover and simmer for 5 minutes.
Stir in tomato pasta sauce and remove from heat.
Spread 1/4 of the artichoke mixture on the bottom of the prepared baking dish.
Top with 3 cooked noodles.
Sprinkle 3/4 cup mozzarella over the noodles.
Repeat layers two more times.
Finish with the remaining artichoke mixture and mozzarella.
Sprinkle crumbled feta evenly over the top.
Cover the dish with foil and bake for 40 minutes.
Remove foil and bake an additional 15 minutes until hot and bubbly.
Let lasagna stand 10 minutes before slicing and serving.