Heat 2 tablespoons oil in 12-inch nonstick skillet over high heat until beginning to smoke; add red pepper and cook until lightly browned, about 2 minutes, stirring only once after 1 minute. Add asparagus, 1/4 teaspoon salt, and 1/8 teaspoon pepper; cook until asparagus is browned and almost tender, about 2 minutes, stirring only once after 1 minute. Stir in shallot and cook until softened and asparagus is tender-crisp, about 1 minute, stirring occasionally. Transfer to large plate and cool 5 minutes.
Meanwhile, whisk remaining 4 tablespoons oil, vinegar, garlic, 1/4-teaspoon salt, and 1/8-teaspoon pepper in medium bowl until combined. In large bowl, toss spinach with 2 tablespoons dressing and divide among salad plates. Toss asparagus mixture with remaining dressing and place a portion over spinach; divide goat cheese among salads and serve.