Yes, Mitsuba is fairly easy plant to grow and I grow them every year at my house.
It can be harvested in indoor, balcony or house garden. Mitsuba is found in a moist, with not much sun lights so not much sun light is needed. It can be even grown on the sponge. Mitsuba has different way of cultivation depending on how you would like to eat it. On this post, I I will write how to cultivate popular way to grow mitsuba.

In many gardening, ito-mitsuba（string mitsuba）, is the most common ones to be grown in home garden. String mitsuba is used in soup as a topping.
Proper time to plant mitsuba seed is spring and fall. Plant seeds in low-alkaline base soil. Though growing mitsuba doesn’t need much sun lights, but light is needed to germinate the seeds so only put a thin layer of soil on seeds. Since you can only put thin layer of soil, please be careful not to let it dry out. If surface of soil gets dry and water is needed, use spray bottler and spray water.
After the seeds germinated, you don’t need much sunlight to grow mitsuba. Once mitsuba grew up to be around 8cm, give liquid fertilizer. This is only needed to be done once every 2 weeks. When mitsuba grow up to 15cm, leave 5cm on the bottom and use it as an herb for cooking.
Even after cutting stem out, mitsuba will re-grow itself right after. However, tastes and smell will go down over time so please plant a new mitsuba every year.