1. Preheat oven to 350 degrees.

2. In a small bowl, whisk mustard, vinegar, and a pinch each of sugar, salt, and pepper together. Continue to whisk while slowly drizzling olive oil in until completely combined.

3. Season chicken on both sides with salt and pepper; set aside.

4. Cut 4 pieces of parchment paper into 16-by-18-inch pieces. Fold each sheet in half lengthwise, then open and place on a work surface. Divide asparagus evenly among the four pieces of parchment; place them on the left side of the fold near the crease, centered evenly between the top and bottom of the parchment paper. Place a chicken breast on top of each bed of asparagus. Drizzle with about 1 tablespoon vinaigrette. Top chicken breasts with tomatoes, olives, artichokes, basil, and feta. Drizzle each with about 1 tablespoon more vinaigrette.

5. Fold the right half of one parchment paper over contents and, starting with the top right corner, form a half-moon packet making small but tight pleats all the way around to seal completely. Repeat process to form remaining packets.

6. Transfer the packets to rimmed baking sheets and cook for 25 to 28 minutes. To serve, place packets directly on each of four plates and use kitchen shears or a sharp knife tip to open packets at the table.