Heat oven to 400°F. Lightly grease a baking sheet.
In a food processor, combine 1 cup loosely packed basil leaves, 2 tablespoons fresh thyme leaves, 1/2 teaspoon dried oregano, 2 chopped garlic cloves, 1/4 teaspoon salt, a pinch of red pepper flakes, and 1/4 cup oil. Process until the herbs and garlic are finely chopped and the mixture comes together, stopping once or twice to scrape down the sides.
Open the 16-ounce can of refrigerated flaky biscuits. Pull each biscuit apart into its layers to create two thinner rounds from each biscuit.
Place the separated biscuit rounds on the prepared baking sheet, a little space apart. Use your fingers to flatten and gently enlarge each round to form a small, even disc.
Spread about 1 teaspoon of the pesto mixture on top of each flattened biscuit round.
Sprinkle 1/4 cup pine nuts and 1/3 cup grated Parmesan cheese evenly over the rounds, pressing gently so the toppings adhere.
Bake for 8 to 10 minutes, or until the biscuit rounds are golden brown. Remove from the oven, let cool slightly, and serve.