Rinse lentils and bring to boil in broth. Simmer, partially covered for 30 min. They should become soft but hold their shape.
While lentils are simmering, heat 2 Tbsp EVOO and sauté the tomatoes at medium for about 25 minutes. The tomatoes should keep their shape but become very soft and their juices should concentrate in the oil.
While the lentils and tomatoes are cooking, chop the carrot and red onion. Wash and slice the basil. Place in medium sized bowl. Set aside.
Prepare the dressing. Whisk another 2 Tbsp of EVOO with the vinegar and Honeycup mustard. (If you don't have Honeycup mustard, use Dijon mustard with about ½ tsp sugar.) Set aside.
Drain lentils. Place in bowl with chopped raw vegetables. Give the dressing a final whisk and pour it over the vegetables. Mix well.
Add the tomatoes. Be sure to include the EVOO and concentrated juices. Mix gently.
Cool slightly (½ hour is about right) and serve at room temperature.