Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add onion; sauté until golden, about 6 minutes.
Add garlic and anchovies; reduce heat to low and cook, stirring, until fragrant, about 30 seconds.
Stir in tomatoes, tomato paste, olives, capers, salt and pepper flakes; bring to a boil over medium-high heat. Reduce heat to low and simmer, stirring occasionally, until slightly thickened, about 6 minutes
Remove from heat; stir in remaining teaspoon oil and parsley (if using).