Put a baking sheet in the lower third of the oven and preheat to 425 degrees F. Whisk the eggs, half-and-half, 3/4 teaspoon salt and ¼ teaspoon pepper in a large bowl and set aside.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the spinach, artichoke hearts and 2 pinches salt. Cook, stirring, until the spinach is wilted and the skillet is dry, about 1 minute. Remove the vegetables to a plate lined with a few layers of paper towels; let cool slightly. Carefully pull up the sides of the paper towels and squeeze out most of the liquid; stir the vegetables into the egg mixture.
Scatter the goat cheese in the bottom of the pie crust. Pour in the egg mixture, then arrange the tomatoes cut-side up in the eggs. Season with pepper. Carefully place the quiche on the hot baking sheet and bake until set, about 30 minutes.
Meanwhile, whisk the vinegar and mustard in a medium bowl; whisk in the remaining 1 tablespoon olive oil until smooth. When the quiche is almost done, add the salad mix to the bowl and toss with the vinaigrette. Season with salt and pepper.
Cut the quiche into wedges and serve with the salad.