Preheat a grill to medium-high.
Drizzle the carrots on a baking sheet with 2 tablespoons olive oil. Sprinkle evenly with salt and use a small strainer to sprinkle evenly with the cumin. Arrange the bell pepper halves cut-side up next to the carrots, then drizzle with 2 tablespoons olive oil, sprinkle with salt and sift with paprika.
Cut the outer layer off the leeks and trim and discard 2 inches off the top. Split the leeks lengthwise and rinse the dirt out from the inside layers. Wipe dry and keep them in intact halves. Drizzle with 2 tablespoons olive oil and sprinkle with salt.
Grill the vegetables (leeks and peppers zucchini cut-side down) in a single layer in a medium-hot area of the grill. Close the lid and cook until you see liquid emerge, 3 to 5 minutes. Turn everything on its second side, then close the lid and cook until the peppers are tender but still hold their shape, 5 to 8 more minutes.
Move the peppers to a cooler or foiled area of the grill, then close the lid and let the carrots and leeks continue to cook until tender when pierced with the tip of a knife, an additional 5 to 8 minutes.
Season the parsley in a bowl with 1 tablespoon olive oil and a pinch of salt. Place the parsley on a medium-hot part of the grill and cook until fairly charred, 10 to 12 minutes. Chop the parsley finely. Drizzle the jalapeno with 1 tablespoon olive oil and grill until charred, 6 to 8 minutes. Remove the jalapeno from the grill and coarsely chop.
Combine vinegar, brown sugar and orange juice in a medium bowl until the sugar dissolves. Whisk in the remaining 3 tablespoons olive oil, the mustard, parsley and jalapeno. Taste for seasoning.
Place the leeks on a flat surface and cut each half into 3 even pieces. Cut the peppers in half again. Arrange the carrots, peppers and leeks on a serving platter and top with the dressing.