Toast almonds in small skillet over medium heat, stirring frequently, until pale golden and fragrant, 2 to 4 minutes. Cool almonds to room temperature.
2. Process cooled almonds, tomatoes, basil, garlic, pepperoncini, 1 teaspoon salt, and red pepper flakes (if using) in food processor until smooth, about 1 minute. Scrape down sides of bowl with rubber spatula. With machine running, slowly drizzle in oil, about 30 seconds.
3. Meanwhile, bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook until al dente. Reserve ½ cup cooking water; drain pasta and transfer back to cooking pot.
4. Add pesto and ½ cup Parmesan to cooked pasta, adjusting consistency with reserved pasta cooking water so that pesto coats pasta. Serve immediately, passing Parmesan separately.