Bring a large pot of salted water to a boil. Add kale to the pot and cook for 4 minutes. Remove kale with tongs, reserving the excess water. Drain kale in a colander and leave it there to cool. Once cool, squeeze kale to let out excess water. You'll be shocked how much water will come out of those leaves! It's like squeezing a sponge! Transfer to a cutting board and finely chop.
(If you're using store bought crumbs you can skip this step altogether.) Meanwhile, heat 3 Tablespoons olive oil in a medium sized skillet over medium heat. Use a food processor to pulse the bread slices into fine crumbs. Add breadcrumbs to the hot oil and stir to coat. Cook for about 4 minutes, stirring occasionally. Add one minced garlic clove to the mixture. Stir and cook for an additional 3-4 minutes or until mixture is browned and crispy. Place crumbs in a bowl or plate lined with a paper towel.
In the same skillet, add butter and remaining 2 Tablespoons olive oil. Add celery and carrots and cook until softened, about 4 minutes. Add remaining minced garlic and red pepper flakes and cook until fragrant, about 1 minute. Add kale and 1/2 cup water to the skillet and cook until heated through, about three minutes. Season with Kosher salt and fresh ground pepper.
Meanwhile, bring the kale water back to a boil and cook the orrechiette according to package directions. Drain orrechiette, but be sure to reserve 2 cups of the pasta water!
Place orecchiette back in the pot then stir in kale and carrot mixture. Add about a 1/2 cup of the pasta water back to the pot and stir to coat. Add cheese and stir. Continue to add additional pasta water until the pasta is well coated and smooth. Divide among bowls, sprinkle with breadcrumbs, and drizzle with additional olive oil if desired.