Toss the slices of summer squash and zucchini in olive oil until fully coated on both sides. Season both sides with salt and pepper to taste.
If grilling, preheat the grill on high direct heat until it hits 500-600 degrees F. Grill the zucchini and summer squash for about 5 minutes per side, until charred and tender. Remove from the heat and cover with foil before proceeding with the orzo.
If roasting, preheat the oven or air fryer to 450 degrees F. Line hte slices of zucchini and summer squash on a sheet pan and roast for about 10-15 minutes, until golden brown and slightly crisp. Flip halfway through to ensure both sides get nice and crispy. Prepare the orzo as the zucchini roasts.
Fill a large stockpot 3/4 of the way full with water. Season with 1 tbsp of kosher salt. Cook the orzo according to the package and drain it 2 minutes before al dente (it will cook residually in the sauce!)
As the orzo cooks, heat a large sauté pan over medium high heat. Add the butter and let it melt, after it's metled, keep a close eye on it to watch the color change from yellow to deep gold/light brown and nutty in fragrance (about 2 minutes or so - don't let it get darker in color or it will burn as it continues to cook.) Once the butter is gold/light brown, adjust the heat to medium low and add the sage. Cook until fragrant. Then, add the lemon zest and lemon juice and stir until a sauce is formed.
Transfer the cooked orzo to sauce and toss until the orzo is fully coated. Add the Parmesan and mix until it's melted and fully incorporated throughout.
Plate the orzo. Top with summer squash and a little more cheese. Enjoy immediately!