Make the field peas Heat oil in a medium saucepan over medium until shimmering. Add onion and garlic, and cook, stirring occasionally, until tender, about 7 minutes. Add peas, 3 cups water, thyme sprigs, salt, and pepper. Bring to a simmer over medium-high. Reduce heat to medium-low, and cook until tender, about 25 minutes. Keep warm over low.
Make the vinaigrette Whisk together vinegar, lemon zest, lemon juice, shallot, salt, and pepper in a small bowl. Let stand 15 minutes. Whisk in mustard, honey, and garlic. Whisk in oil in a slow, steady stream until emulsified. Bring 8 quarts water to a simmer in a large stockpot over medium-high. Prepare an ice bath in a large bowl. Add sausage links to simmering water; reduce heat to medium-low, maintaining water temperature between 160°F and 170°F. Poach sausages until cooked through and a thermometer inserted in sausage registers 135°F, 6 to 8 minutes. Immediately transfer sausages to ice bath, and let stand until completely cool, about 10 minutes. Cut sausages between links. Let stand at room temperature while grill preheats, about 30 minutes.
Open bottom and top vents of a charcoal grill completely. Light charcoal chimney starter filled halfway with briquettes. When briquettes are covered with gray ash, pour onto one side of bottom grate of grill.
Place sausages on oiled grate over side with coals, and grill, covered, just until grill marks appear, about 2 minutes per side. Using tongs, gently move sausages to side of grill without coals, and grill, covered, until a thermometer inserted in sausage registers 145°F, 5 to 6 minutes. (If fire starts to flare up, move sausages or spritz coals with water. Resist the urge to grill quickly, as high heat will make the sausages burst.) (If using a grill pan, heat pan over medium-high, and lightly grease.
Grill sausages until grill marks appear on both sides and a thermometer registers 145°F.)
Assemble the dish Drain warm field peas; discard liquid. Toss peas with 1/2 cup vinaigrette. Serve grilled sausages overdressed field peas; garnish servings with baby mustard greens. Drizzle with additional vinaigrette to taste.