Using a vegetable peeler, peel one strip off of the first squash, lengthwise. Discard first strip (since it’s all skin). Rotating the squash, continue peeling the squash so each strip has a thin sliver of skin. Once there is no skin left, use the peeler to slice around the remainder of the squash until you hit the seeds. Repeat with other two squashes.
In a large pan over medium heat, heat enough oil to cover the bottom of the pan. Add garlic and red pepper flakes, and cook for 2-3 minutes. Once the garlic starts to turn golden, add the slivers of squash and a dash of salt and pepper. Using tongs, toss to coat and drizzle a little more oil if the squash looks dry. Cook for 3-4 minutes until the slivers start to wilt. At this point, add the tomatoes and cook for an additional 2-3 minutes.
Remove the pan from heat and immediately stir in ricotta and fresh basil. Use the tongs to work the ricotta into a sauce, ensuring each strand of squash is coated.