Preheat oven to 250°. Prepare an ice bath with ice cubes in cold water in a medium-sized bowl.

Bring a large saucepan of water to a boil. With a sharp paring knife, carefully core each tomato. Score the opposite end gently, just breaking the skin. Place tomatoes in a large heatproof bowl.

Pour boiling water over tomatoes; let soak 30 seconds. Remove with a slotted spoon, and place in ice bath to cool quickly. Remove after 2 minutes.

Peel tomatoes when cool enough to handle. Cut in half lengthwise, and place, cut side up, on a parchment-lined baking sheet. Drizzle evenly with olive oil; season with salt, pepper 
and thyme.

Roast until tomatoes are dried halfway through, 5–6 hours. Let stand to cool. At this point, you can cut or blend them up slightly to make more of a jam-like consistency. To store, place in a sealable container. Pour oil from baking sheet over the top. Refrigerate up to 1 week.

Wash asparagus with cold water. Remove woody stems by peeling the last 2–3 inches of each spear, and then slicing off tips on a bias to make a pointed end.

In a small bowl, whisk together remaining ingredients until well-combined. Toss trimmed asparagus into mixture until well-coated.

Cook asparagus outside on a grill in a grilling basket, about 3 minutes, or on a sheet pan at 400° for 15 minutes, until tender.