In a large deep skillet or wide pot, combine the tagliatelle pasta, vegetable broth, water, olive oil, sliced garlic, halved cherry tomatoes, salt, black pepper, dried oregano, and red pepper flakes.
Bring the mixture to a boil over medium-high heat, stirring occasionally to prevent the pasta from sticking.
Once boiling, reduce the heat to medium and simmer uncovered, stirring frequently, until the pasta is al dente and most of the liquid has been absorbed, about 10 to 12 minutes.
Add the fresh baby spinach to the pot and stir until wilted, about 2 minutes.
Remove the pot from heat and stir in the grated Parmesan cheese until well combined.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve immediately, garnished with extra Parmesan cheese if desired.