Remove the tough stems from the kale and tear the leaves into 2-inch pieces, then rinse thoroughly and set aside to drain slightly. While the kale drains, fill a large pot with salted water and bring it to a rolling boil—this allows the kale to be ready to cook as soon as you need it, and the boiling water will be perfectly timed for the pasta.
Add the linguine to the boiling salted water and cook for about 7 minutes, or until just tender but still with a slight bite (al dente). Reserve 1/4 cup of the pasta cooking water before draining—this starchy water is liquid gold for helping the sauce coat the pasta evenly. Drain the pasta and set it aside.
In a large, wide pan, combine the olive oil, butter, and thinly sliced garlic over medium heat, cooking gently for 1-2 minutes until the garlic becomes fragrant and just barely golden—don't let it brown or it will taste bitter. Add the torn kale directly to the pan and cook for 5-7 minutes, stirring occasionally, until the leaves are completely wilted and tender. I like to add the kale in batches if needed, letting earlier batches wilt before adding more, which ensures even cooking and prevents the pan from becoming overcrowded.
Add the drained pasta from Step 2 to the wilted kale in the pan and toss gently to combine. Pour in a splash of the reserved pasta water (about 2-3 tablespoons) to create a light, silky coating that brings everything together. Remove from heat and let the mixture cool for 1-2 minutes until the steam subsides, then taste and add the salt and black pepper to your preference. Finish by sprinkling the grated Parmesan cheese over the top and tossing once more to distribute it evenly. I find that adding the cheese after removing from heat keeps it from clumping, and the gentle residual warmth melts it perfectly into the pasta. Top with the red pepper flakes for a gentle kick of heat and color.