To make the parsnip noodles: Peel the parsnips. Use a vegetable spiralizer to make fettuccine-sized noodles. Or use a vegetable peeler to shave the parsnip into strips.
Heat the olive oil in a large skillet over medium-high heat. Add the crumbled tempeh, season with a little salt and pepper, and cook, stirring often, until the tempeh is browned on all sides, about 4 minutes.
Add the garlic and cook, stirring often, until the garlic is fragrant, about 30 seconds more. Add the parsnip “noodles,” cherry tomatoes, basil, tomato paste, and stock, and toss to combine.
Turn the heat down to medium-low and cook, stirring occasionally, until the liquid is evaporated, the parsnip noodles are cooked but still al dente, and the tomatoes are soft, about 3 minutes.
Add the crumbled goat cheese, toss to combine, and serve immediately.