Preheat oven to 350 degrees.
Place pan over medium heat. Add oil, garlic and spinach. Cook for about 5 minutes. Set aside.
Boil pasta noodles following box instructions. Set aside.
For the sauce:
Blend milk and cooked cauliflower in a blender until smooth. Set aside.
In a pot, melt butter over medium heat. Add flour and whisk for 30 seconds. The mixture should stay white. Slowly add the milk mixture while constantly whisking. Bring to a boil. Be sure to keep stirring so the bottom does not burn. Add spinach and season with salt and white pepper. Stir well.
Assembling in a 9x9 pan will make about 4 layers.
Spread a thin layer of sauce on the bottom of the pan. Lay out the pasta with the sides slightly overlapping.
Spoon ricotta and lightly spread over pasta. Sprinkle the artichoke and broccoli evenly, then each of the cheeses. Press down the layer firmly with your hands, then spread sauce.
Repeat, the steps starting with the pasta and making sure to press down each layer as you go.
Skip the sauce on the second to last layer and instead layer pasta. This will be your top pasta layer. Spread the rest of your sauce and ricotta over the pasta. Sprinkle the remaining cheeses evenly.
Cook in the oven for about an hour uncovered. If top starts becoming too dark, cover with foil and continue cooking until sauce is bubbling on the sides. Let lasagna rest for 15 minutes before enjoying!