Both Brussels Sprouts and Green Beans benefit from being parboiled prior to sauteing. It helps speed the cooking process while softening them up so they will better absorb the other flavors in the dish. If you use a slotted spoon to remove them, you can use the same pot of water.
Bring a large pot of water with 1 T. salt to a boil.
Cut 1 lb. worth of Brussel Sprouts in half from top to bottom.
Trim the ends of 1/2 lb. Green Beans.
Make an ice water bath in a large bowl.
Drop the sprouts in the water. When the water returns to a full, rolling boil, remove them with a slotted spoon and transfer into the ice-water bath. When they cool, remove them again into a colander.
Repeat the process with the Green beans.
You can parboil the vegetables up to a day ahead.
In a large skillet, heat 3 T. olive oil. Add 1 C. sliced onion, slices cut in 2″ pieces. Add 1 1/2 t. fennel seeds. Saute until the onion is nicely browned.
Add the vegetables along with 1/4 C. pine nuts, chopped almonds, or chopped walnuts. Add salt and pepper to taste.
Saute until the vegetables are lightly browned, 3-5 minutes. Add 4 T. lemon juice, turn off the heat and stir to combine. Top with 1/3 C. grated parmesan cheese.