Whisk together eggs, milk, chives, ¼ teaspoon of salt, and pepper in a large bowl.
Heat olive oil in a medium-size cast-iron skillet (or other oven-proof skillet) over medium high heat.
Add the onion and remaining ¼ teaspoon salt to the skillet; cook, stirring occasionally, until softened (about 6 minutes). Add the garlic, and cook, stirring constantly, until fragrant (about 1 minute). Reduce the heat to medium-low, and slowly pour the egg mixture into the skillet; sprinkle with the cheddar cheese. Cook, stirring constantly, just until the mixture begins to set (about 1 minute). Continue to cook, undisturbed, until mostly set (about 8-10 more minutes).
Meanwhile, preheat the broiler. Transfer the frittata in the skillet to the preheated oven, and broil 6 inches from the heat until the top is lightly browned (about 2 minutes). Slice into 4 quarters and serve immediately, or allow to rest at room temperature for an hour or two before serving.