Pat salmon filets dry. Season with dried oregano, salt, and pepper.
Whisk together balsamic vinegar, honey, and peach jam.
In an oven-safe skillet, heat 2 tablespoons olive or avocado oil over medium. Sear salmon filets 4-5 minutes per side until the skin crisps and the salmon begins to flake.
Add butter in the skillet and swirl to evenly melt. Cook 2-3 minutes until butter browns. Baste salmon constantly with the butter.
Pour in honey balsamic mixture and bring to a boil. Cook until reduced by half, about 4-5 minutes, spooning the sauce over the fish.
Remove skillet from heat. Arrange peaches and tomatoes evenly around the salmon. Broil 1-2 minutes until peaches soften and tomatoes begin to burst. To serve, place feta all around the pan and top with fresh basil leaves.