1. Heat butter with 1 1/2 tablespoons oil in a 10-inch ovenproof nonstick skillet over medium-low heat until melted.

2. Preheat broiler, with the rack about 7 inches from heat source. Meanwhile, whisk together eggs, cream, and herbs until well blended. Stir in the salt, and season with pepper.

3. Add egg mixture to skillet; cook until bottom is set and golden, about 4 minutes. Continue to cook, gently shaking pan occasionally, until 1 inch of the edges is almost set, about 4 minutes more. Remove from heat. Gently press zucchini and squash on top, overlapping slightly in concentric circles.

4. Broil (checking often) until golden and just cooked through in center, 1 to 2 minutes. Gently slide onto a plate with a spatula; drizzle with remaining tablespoon oil. Garnish with whole chives.