Rinse and dry the produce. Fill a large pot with water, season with salt, and place over high heat. Thinly slice the asparagus on the diagonal. Trim the ends of the patty pan squash and small dice. Peel and mince the shallot.
Place a large skillet over medium heat. Add the walnuts and cook, shaking pan frequently, until nuts are fragrant and toasted, about 2 to 4 minutes. Transfer to a plate to cool. Combine the diced patty pan squash, minced shallot, toasted walnuts, and 1 tbsp olive oil in a medium bowl. Zest the lemon, and add to to the bowl with a pinch of salt and pepper. Stir relish well to combine.
In a food processor, combine the basil, spinach, garlic, almonds, and ¼ cup water. Pulse 3 to 4 times to mix everything together. Turn processor on high, and with motor continuously running, slowly add 3 tbsp olive oil. When the pesto is done, it will be well mixed but still have some texture. Season with salt and pepper.
Once the water is boiling, add the Banza penne, stir, and cook until al dente, about 6 to 8 minutes. Reserve ½ cup of the cooking liquid and drain the pasta in a colander.
Wipe the large skillet clean, return to medium-high heat and add 1 tbsp olive oil. Once hot, add the sliced asparagus and cook until bright green and just tender, about 2 to 3 minutes. Add the cooked penne, pesto, and half of the reserved pasta water. Toss pasta to combine with pesto and cook until warmed through, about 3 to 4 minutes. Season with salt and pepper.
If you prefer your pesto sauce thinner, add the remaining reserved pasta water. Divide the pesto penne between your plates and top with patty pan relish. Halve the lemon and top each portion with a squeeze of juice if desired.