Bring a medium saucepan of water to a boil. Put the broccoli florets in the boiling water and cook for 30 seconds to 1 minute or until the stems are bright and green. Remove from the water with a slotted spoon or strainer and set aside.
Bring the water back to a boil and cook the soba noodles according to package directions.
Meanwhile, melt 1 tablespoon of butter and olive oil together in a large sauté pan over medium high heat.
Add the shiitake mushrooms and cook without stirring for 2-3 minutes, watching so the mushrooms don’t stick to the pan or burn. Stir and reduce to the heat to medium then add the broccoli and the ponzu and cook together for 2-3 more minutes.
Add the remaining tablespoon of butter, stir and season with kosher salt and freshly ground black pepper. Garnish with lemon zest and sesame seeds and add more ponzu to taste.
Fill bowls with portions of soba noodles and top with the broccoli and mushrooms. Or, mix the noodles into the pan with the broccoli and mushrooms, stir, and serve together.
