Preheat the oven to 450°F (232°C). Line a baking sheet with foil and lightly spray or oil it.
In a food processor or blender, combine 1 cup chopped parsley, 1/2 cup chopped basil, 1 clove minced garlic, 1½ cups breadcrumbs, 2 tablespoons olive oil, and 1 teaspoon salt; pulse until the mixture is evenly minced and holds together when pressed.
Place the 4 salmon fillets on the prepared baking sheet. Spread about 1/2 tablespoon Dijon mustard over the top of each fillet in a thin, even layer.
Top each mustard-coated fillet with a heaping spoonful of the herb-breadcrumb mixture, pressing down firmly to form an even crust.
Arrange the 2 cups cherry tomatoes around the salmon on the baking sheet and season salmon and tomatoes with kosher salt and freshly ground black pepper to taste.
Bake the salmon and tomatoes in the preheated oven for 15–20 minutes, or until the salmon is opaque and flakes easily with a fork.
Meanwhile, bring 4 cups water to a boil in a large heavy saucepan. Season with salt and pepper to taste.
Slowly whisk in 1½ cups yellow corn polenta, reduce heat to a simmer, and cook 15–20 minutes, stirring frequently, until the polenta is thickened and creamy.
Remove the polenta from the heat and stir in 5 ounces goat cheese until melted and smooth. Adjust seasoning if needed.
Spoon polenta into bowls, top with a salmon fillet and roasted cherry tomatoes, and serve immediately.