Pat the salmon fillet completely dry with a paper towel and season both sides with sea salt and black pepper.
Heat 1 teaspoon of olive oil in a non-stick skillet over medium-high heat until the oil shimmers.
Place the salmon skin-side down in the pan and press gently with a spatula for 10 seconds to ensure even contact.
Sear for 4-5 minutes until the skin is crispy, then flip and cook for an additional 2-3 minutes until the salmon is just opaque and golden.
Remove the salmon from the pan and set it aside to rest on a plate.
In the same skillet, add the remaining teaspoon of olive oil and the trimmed green beans.
Sauté the beans for 5-6 minutes, stirring occasionally, until they are tender-crisp and slightly blistered.
Add the minced garlic, lemon juice, and lemon zest to the beans, tossing for 1 minute until highly fragrant.
Plate the salmon alongside the zesty green beans and serve immediately.