Preheat oven to 400 degrees F. Line two baking sheets with parchment paper.
Make tomato marinade. Heat 2 tablespoons olive oil in a small saute pan over medium heat. Add anchovies and cook until they start to dissolve, stirring frequently.
Add tomato paste, stirring to combine. Add garlic and coriander and saute for 1 more minute, stirring constantly. Remove from heat and add lemon zest and honey. Let cool completely.
While tomato marinade is cooling, prepare tomatoes. Lay lemon slices in an even layer on one of the prepared baking sheets. Arrange thyme on top and spread tomatoes in an even layer. Drizzle remaining 2 tablespoons olive oil and season with salt and pepper. Roast tomatoes for 20-25 minutes or until lightly charred and tomatoes are softened.
Remove thyme and transfer tomatoes to a bowl. Lightly mash tomatoes with a fork and add basil, parsley, pine nuts, and balsamic vinegar. Mash roasted lemon slices and pour the juices into the bowl with the tomatoes. Season sauce with salt and pepper and set aside.
Season salmon with salt and pepper. Spread tomato marinade on top in an even layer and lay salmon on the other prepared baking sheet. Roast salmon with 15-17 minutes or until flesh flakes easily. Transfer salmon to a serving platter and top with roasted tomato sauce. Serve immediately.
Notes
The tomato sauce and tomato marinade can be prepared the day before.