Start by setting your vegetable stock to simmer in a separate pot. It has to be hot by the time you add it to the rice.
In a medium or large pan, over medium/high heat add the olive oil and once it's hot, add the shallots, making a soffritto.
Once the shallots are translucent, add the arborio rice and fry it with the soffritto so all the grains get coated in the fat.
Reduce the heat to medium low.
Add the white wine and cook until it evaporates completely.
Add the first cup of vegetable stock and cook, stirring occasionally (and gently) until it is absorbed by the rice.
Repeat the process with the other 2 cups of stock, one at a time. If at the end, you think your rice is still too hard, add one more cup of stock and cook until it's al dente.
Turn the heat off and add the butter, stirring vigorously but being careful to not break the grains.
Once the butter has been added and stirred, add the tomatoes and the arugula and stir until everything is incorporated.
Add the fresh mozzarella and stir gently.
Taste to check seasoning and add salt if necessary.
Serve immediately, with freshly grated Parmigiano Reggiano.