Choose pieces of fish that are the same size and thaw fish overnight.
Adjust the oven rack to the upper third and preheat the oven to 450℉.
Toss cherry tomatoes with 2 tablespoons olive oil, five sprigs of fresh thyme, salt, and pepper on a lined, rimmed baking sheet.
Roast tomatoes for 20-25 minutes until the tomatoes become blistered and beginning to burst. Set aside.
While the tomatoes are cooking, season the parsnips with salt and place them in a medium pot. Add half-and-half, garlic, a bay leaf, and the rest of the thyme, and place the pan over medium heat.
Bring to a simmer, cooking for 12-15 minutes or until tender.
Transfer parsnips to a food processor using a slotted wooden spoon, reserving the remaining half and half.
Add the butter and enough half-and-half to create creamy mashed parsnips. The consistency should be like creamy mashed potatoes. Season to taste with kosher salt and black pepper. Keep warm.
Remove the fish from the packaging, gently rinse it, and pat it dry with a paper towel. Season both sides of the fish with salt and black pepper.
In a large skillet over medium-high heat, add 1 tablespoon of olive oil and heat until the oil is shimmering. It's important that the pan is very hot before adding the fish as the heat breaks the protein bonds so the fish won't stick to the bottom of the pan.
If the fish has skin, place it in the pan skin side down. I placed skinless fish fillets in the hot pan and cooked them undisturbed until golden brown, about 2-3 minutes.
Gently flip the fish over and cook another 3-4 minutes. The fish is done when it reaches an internal temperature of 140º. You can tell when it's done as it goes from opaque to white. Serve the fish over a spoonful of parsnip purée, along with greens, lemon zest, lemon slices, cherry tomatoes, and a drizzle of olive oil. Just before serving, squeeze lemon juice over the fish.