Place the mascarpone, 1 cup of heavy cream, powdered sugar, and vanilla extract in a large mixing bowl. With a handheld mixer, mix the ingredients on low speed until the mascarpone is well combined with the heavy cream, but the mixture is still a little soupy.
Increase the mixer speed to medium and mix until soft peaks form (i.e., when you lift the whisk out and hold it upside down, a peak of cream flops over itself), 2 minutes.
Be careful not to overmix the mascarpone or it will turn grainy. Add the remaining 1/4 cup of heavy cream and whip it in by hand with a hand whisk until the cream has thickened and the mixture is smooth and creamy, but seems a little too soft to pipe.
NOTE: The cream is added in two parts to keep from overmixing the mascarpone. If you accidentally over-whip the cream and it turns grainy after adding the remaining heavy cream, add another 1/4 cup of heavy cream and gently whisk it in with a hand whisk until it smooths back out again.
The cream may not seem thick enough to pipe onto a cupcake, but it will thicken more as it sits in the bowl and hold its shaped as it’s piped.
Use the whipped mascarpone immediately or refrigerate it in an airtight container. When you remove it from the refrigerator, put it in a mixing bowl and whisk it by hand until it is smooth again and pipeable, about 30 seconds. If it still has a grainy texture after mixing it, add 1/4 cup of cold heavy cream and whisk the cream in by hand until the mixture has thickened and is smooth again.