Preheat the oven to 375ºF. Brush both sides of baguette slices with olive oil and arrange on a baking sheet. Bake for 8-10 minutes until golden and crisp.
In a food processor, combine goat cheese, cream, lemon zest, chives, parsley, salt, and pepper. Blend until smooth and whipped.
In a small bowl, combine tomatoes, olive oil, vinegar, chives, salt, pepper, and a pinch of lemon zest. Toss to combine evenly. Let sit at room temperature for 20-30 minutes to marinate.
Spread goat cheese onto cooled crostini. Top with marinated tomatoes allowing juice to run off before spooning on to crostini. Serve immediately.