1. To make the pesto, preheat the oven to 375F (190C). Pour the walnuts onto a rimmed baking sheet. Toast the nuts in the oven until they turn a shade or two darker and are fragrant, 6-8 minutes. Pour the nuts onto a plate to cool.
2. Finely grate the zest from the lemon (reserve the fruit for another use). In the bowl of a food processor, combine the toasted walnuts, lemon zest and garlic and pulse just to combine. Add the basil and arugula leaves and process until coarsely chopped. With the machine running, slowly pour in the 1/4 cup of oil. Continue to process until the mixture is moist and well blended but still slightly chunky. Transfer the pesto to a small bowl and taste. Adjust the seasonings with salt and pepper.
3. Warm a saute pan or frying pan over medium-high heat, ad add 1 tbsp of oil. Add the tomatoes and a pinch of salt and petter and saute until the tomatoes are warmed through and their skins are just beginning to split - 3 - 4 minutes. Remove from heat and stir in the pesto.
4. Transfer the tomatoes to a serving dish and crumble the cheese over the top. Server warm or at room temperature.
NOTE: YOU CAN JUST USE A STORE BOUGHT PESTO IF YOU'RE NOT INTO MAKING YOUR OWN.