Heat a drizzle of olive oil in a large pot over medium-high heat. Add sliced onions and cook, stirring occasionally, for 2-3 minutes.
Reduce heat to medium-low, cover the pot, and caramelize onions for 20-25 minutes, stirring occasionally. Remove the lid, add a pinch of salt, and continue cooking another 15-20 minutes until deeply caramelized.
Stir in 1 tablespoon butter and 1 cup of red wine. Increase heat to medium and cook until wine is mostly evaporated.
Add tomato paste, balsamic vinegar, soy sauce, garlic, and anchovies. Cook over medium-high heat, stirring until liquids absorb and garlic is fragrant.
Pour in remaining red wine.
Add canned tomatoes, chicken broth, dried basil, oregano, and sugar. Bring to a simmer, cover, and cook on medium-low for 30 minutes, stirring occasionally.
Use an immersion blender (or transfer to a blender) to puree soup until smooth. Return to pot.
Stir in heavy cream and simmer for 5 more minutes.
Season with salt and pepper to taste. Remove from heat and stir in remaining butter.
Serve garnished with fresh chives, additional parmesan (optional), and freshly ground black pepper.