Pat the salmon fillets dry with paper towels and season both sides with salt, pepper, and dried oregano.
Heat olive oil in a large skillet over medium-high heat.
Place salmon in the skillet skin-side up (if skinless) or flesh-side down. Sear for 4-5 minutes until golden and crisp.
Flip the fillets and cook for another 3-4 minutes until just cooked through. Remove salmon from the pan and set aside on a plate.
In the same skillet, melt the butter over medium heat. Add the minced garlic and cook for 1 minute until fragrant.
Stir in the broth and let it simmer for 2 minutes to deglaze the pan.
Lower the heat and whisk in the heavy cream, lemon juice, and lemon zest. Simmer gently for 3-5 minutes until the sauce slightly thickens.
Add the chopped parsley to the sauce and season with extra salt or pepper if needed.
Return the salmon fillets to the skillet, spooning the creamy sauce over them.
Garnish with fresh lemon slices and serve immediately.