Preheat your oven to 300 degrees Fahrenheit. In a small baking dish, combine cherry tomatoes, 2 cloves smashed garlic, 1/4 teaspoon red pepper flakes, and all of your olive oil. Add salt and pepper to taste and gently toss or stir to combine.
The dish should be tight enough that most of the tomatoes are submerged in oil. If some are poking out that's okay, but if most are poking out, transfer to a smaller baking dish or add more oil.
Place dish into preheated oven and cook uncovered until tomatoes are perfectly tender and the skins have burst, about 90 minutes. You can do this part in advance and store the cooked tomatoes in the fridge until you are ready to eat. They will keep for about a week, although I doubt you'll make it that long!
While the confit cooks, read a book, listen to a podcast, or call a friend. This is also a great time to prep your kale, parsley, and the remaining 4 cloves of garlic.
Once the tomatoes are done, bring a large pot of heavily salted water to boil, and cook the pasta 2 minutes shy of the package recommendation for al dente. Be sure to save 1/2 cup of pasta water.
In the meantime, in a large skillet over medium heat, spoon 2 tablespoons of olive oil from your tomato confit into the pan. Add breadcrumbs and season with salt and pepper. Toast the breadcrumbs in the oil, stirring frequently until golden brown and crunchy enough that you can hear them scrape against the bottom of the pan, about 5 minutes. Once breadcrumbs are browned, set aside on a small plate.
Wipe out the pan, ensuring no crumbs are left (otherwise they will burn!) and spoon in 3 tablespoons of confit oil. Over medium heat, combine anchovy filets, sliced garlic, and remaining 1/2 teaspoon of chili flakes. Season with salt and pepper. Saute the anchovy garlic mixture until the anchovies have fully disintegrated, about 2 minutes. Add in kale and 1-2 tablespoons of tomato confit oil. Season with salt and pepper. Cook until kale is wilted and beginning to crisp, 5-6 minutes.
Turn the heat to low and add pasta, reserved 1/2 cup pasta water, and 2 tablespoons of confit oil. Stir the mixture vigorously until the water has mostly evaporated and the sauce looks glossy. Turn off the heat. Use a slotted spoon to remove tomatoes from the oil and place them into the pan. Add parsley, and gently stir the pasta mixture to ensure tomatoes do not burst.
To serve, top with a drizzle of confit oil, breadcrumbs, reserved parsley, and flaky salt.