Slice the cherry tomatoes in half, and arrange them, cut sides up, on a baking sheet. Sprinkle them with salt, pepper, and the bay leaf; drizzle with 1/4 cup olive oil.
Bake the tomatoes until they are shriveled and dry on the outside, but a little moist inside, about 2 hours.
Toast the pine nuts in a small pan over medium-low heat, gently shaking the pan as they toast, until beginning brown and fragrant, 2 to 3 minutes; set aside.
Bring a saucepan of water to a boil; cook the green beans in the boiling water until bright green but still crisp, about 3 minutes. Drain and rinse immediately with cold water.
Combine the roasted tomatoes, toasted pine nuts, green beans, arugula, and basil in a salad bowl. Whisk together the red wine vinegar, mustard, garlic, honey, and 1/4 cup olive oil in a bowl, and pour the dressing over the salad. Stir in the crumbled feta cheese just before serving.