Heat olive oil in a large skillet over medium-high heat until shimmering. Add diced onion and sauté for 3 minutes until softened, then add minced garlic and cook for another 30 seconds until fragrant.
Add halved baby potatoes to the skillet and stir to coat with oil. Cook for 8-10 minutes, stirring occasionally, until potatoes begin to soften and develop light golden edges on the exterior.
Pour in vegetable broth and bring the mixture to a gentle simmer. Season with dried dill, salt, and pepper, then nestle the salmon fillets skin-side down into the liquid among the potatoes.
Cover the skillet and simmer for 12-15 minutes until the salmon flakes easily with a fork and reaches an internal temperature of 145°F. This cozy salmon skillet dinner comes together beautifully when you don't rush this crucial step.
Remove the skillet from heat and scatter fresh spinach over the top, allowing residual heat to wilt it gently. Add halved cherry tomatoes, squeeze fresh lemon juice over everything, and dot with butter.
Stir gently to combine, allowing the butter to melt and coat the vegetables. Taste and adjust seasoning as needed, then garnish with lemon zest and fresh chopped parsley before serving immediately.