Season salmon with oregano, salt and pepper. In a large skillet over medium heat, add 1 tablespoon olive oil. When oil is shimmering but not smoking, add salmon skin-side up and cook until deeply golden, about 6 minutes. Flip and cook 6 minutes, until salmon is opaque and flakes easily. Transfer to a plate.
Add remaining tablespoon olive oil to skillet, then stir in garlic and shallots. Cook until garlic is fragrant, about 1 minute. Add tomatoes and season with salt and pepper. Cook, stirring frequently, until tomatoes just begin to burst. Remove from heat and squeeze lemon juice on tomatoes.
Serve salmon with tomato mixture spooned on top. Garnish with basil and Parmesan, then drizzle with balsamic glaze if desired. Serves 4.
Balsamic Glaze (optional):
In a small saucepan over medium heat, add balsamic vinegar and honey and simmer until reduced by half; set aside.
Approximate Nutrient Analysis per serving (not including salt to taste, and not including glaze and parmesan cheese):
450 calories, 30 g fat, 6 g saturated fat, 95 mg cholesterol, 115 mg sodium, 7 g carbohydrate, 2 g fiber, 4 g sugar, 36 g protein