Preheat the oven to 400℉.
Halve the potatoes then toss in 1 TB vegetable or olive oil and season with salt and black pepper to personal preference.
Oil the sheet pan with 1 TB of oil. Add the potatoes cut side down and bake for 25 minutes.
When the time is up, toss the broccoli in 1 TB of oil, then add salt and pepper as well. Flip the potatoes over then place on the sheet pan with the potatoes.
Cook the potatoes with the broccoli for the remaining 20-25 minutes.
Remove from the oven. Before serving garnish with lemon zest and toss in lemon juice.