Add flour, butter, thyme, rosemary, 1/2 teaspoon salt, and 1 egg to the mixing bowl. With the measuring cup, process for 30 seconds / speed 4 until dough comes together.
Transfer dough to a piece of plastic wrap, press into a disc, wrap tightly, and refrigerate for 30 minutes. Wash and dry the mixing bowl.
Preheat the oven to 190°C | 375°F. Scatter the thyme and cherry tomatoes over the sheet pan. Add 3 unpeeled garlic cloves. Drizzle everything with olive oil, sprinkle salt and pepper.
Shake the pan back and forth to spread out the oil and seasonings and coat the tomatoes. Roast for 30 minutes or until the tomatoes start to shrivel.
Reserve the garlic and discard the thyme. Place the tomatoes in a fine sieve set over a bowl and let it drain.
Add remaining 2 eggs and cream to the mixing bowl. Mix for 25 seconds / speed 5.
Peel the roasted garlic cloves and add the garlic to a small bowl with the goat cheese. Use a fork to mash garlic into goat cheese.
Change the oven temperature to 200°C | 400°F. Spray a 24cm (9.5-inch) tart pan with a removable bottom with cooking spray.
Roll out the pastry dough on a lightly floured countertop and gently pressing the dough into the edges of the pan and up the sides. Roll the rolling pin over the top of the tart pan to cut off any excess dough.
Crumble the goat cheese over the bottom of the crust and top with the tomatoes. Pour the egg-cream mixture over the top. Bake on the middle rack of the oven for 30 minutes or until set and lightly browned. Clean the mixing bowl.
Pick parsley, mint, and basil leaves. Peel the remaining garlic. Rinse capers and anchovies, pat dry. Add herbs, garlic, capers, anchovies, vinegar, remaining olive oil, remaining salt and pepper to the mixing bowl.
Purée for 10 seconds / speed 8. Scrape down the sides of the mixing bowl.
Purée again for 10 seconds / speed 8.
Let the tart cool for 15 minutes, then remove the pan ring. Serve the tart with the salsa verde.
Enjoy your meal!