Bring a pot of water to a boil. Cook the ravioli in the boiling water according to the package instructions.
Meanwhile, melt the butter in a large skillet over medium-high heat and add the garlic and onions. Cook, stirring, for 1 minute. Add the broccoli and asparagus and cook, stirring, 1 minute. Season with salt and pepper. Splash in the broth, then cook until the liquid reduces a bit, 2 to 3 minutes. Stir the cream into the skillet and reduce the heat to a simmer. Stir in the ham, Parmesan and pesto and cook for a couple of minutes to allow the sauce to thicken.
Drain the ravioli, then add them to the sauce with the tomatoes and toss. Sprinkle with the basil and extra Parmesan before serving. Enjoy.