Heat grill to medium. In a large bowl, combine asparagus, scallions, and 1 tablespoon sun-dried tomato oil; season with salt and pepper. Grill, turning occasionally, until vegetables are tender, 6 to 9 minutes. When cool enough to handle, cut asparagus and scallions into thirds.
Brush a large baking sheet with 1 tablespoon sun-dried tomato oil. On a lightly floured work surface, divide dough in half. Roll or stretch to form two 9-inch ovals. Transfer to prepared sheet, and brush with remaining tablespoon sun-dried tomato oil.
Transfer dough pieces to grill. Cook until undersides are firm and beginning to char, 2 to 3 minutes. Using tongs or a large spatula, transfer crusts, grilled side up, back to baking sheet.
Dividing evenly, top crusts with ricotta, then asparagus, scallions, and sun-dried tomatoes; season with salt and pepper. Slide back onto grill and cook, rotating occasionally, until crusts are cooked through and cheese is melted, 3 to 5 minutes. Transfer pizzas to a cutting board, cut in half, and serve.