Roast in the preheated oven until pine nuts are toasted and fragrant, 5 to 10 minutes.
Heat olive oil in a skillet over medium heat; cook and stir garlic until lightly golden brown, about 5 minutes. Combine 3 tablespoons olive oil mixture, 1 1/2 teaspoons dill, 1 teaspoon sea salt, and 1/2 teaspoon lime juice in a large bowl; add broccoli and toss to coat. Spread broccoli onto a baking sheet.
Roast in the preheated oven until broccoli is slightly tender, 15 to 20 minutes.
Heat remaining olive oil mixture in skillet over medium heat; cook and stir tomatoes, remaining 1/2 teaspoon dill, remaining 1/4 teaspoon salt, 1/2 teaspoon lime juice, and honey until tomatoes softened, about 3 minutes. Mix vinegar and basil into tomato mixture until dressing is evenly combined; remove skillet from heat.