Preheat broiler with rack in top third. Heat 1 tablespoon oil and garlic in a 10-inch broilerproof nonstick skillet over medium. When fragrant, add chard stems and leaves. Season with salt and cook, stirring, until just tender, 4 minutes. Transfer to a bowl.

In a large bowl, whisk together eggs, milk, 1 teaspoon salt, and 1/8 teaspoon pepper until well combined. Stir in rye berries, chard leaves and stems, and all but 1 tablespoon combined chopped herbs and scallions.

Return skillet to medium-high heat; add remaining 1 tablespoon oil. Add egg mixture and cook, stirring with a spatula to create large curds, until eggs are just beginning to set, about 3 minutes. Remove from heat, dollop with ricotta, and transfer to oven. Broil until eggs are puffed, just set, and beginning to brown in spots, 2 to 3 minutes. Let stand 10 minutes. Garnish with remaining chopped herbs and scallions, and serve warm or room temperature.