In a mixing bowl, combine the butter, 2 tbsp. Thai basil, sundried tomatoes, lemon juice and zest, garlic, 2 tbsp. Italian parsley and 1 tbsp. Parmesan cheese. Form the compound butter into a block and wrap well in parchment paper. Label and date your package and place into the freezer.
Preheat oven to 350°F. Cut squash in half lengthwise and discard the seeds. Rub the inside of each half of the squash with 1 tbsp. olive oil and season with salt and pepper. Place the squash onto a parchment paper-lined sheet pan, skin side up and roast in the oven for 10 to 12 minutes, or until tender. Shred with a fork. Cool until easy to handle. Using a long fork, scrape the squash to make thin strands that resemble spaghetti noodles. Place in a bowl, then into the refrigerator to cool.
Add 1 tbsp. olive oil to a large sauté pan over medium-high heat. Add the chilled spaghetti squash and cook for 1 to 2 minutes. Add 1 tbsp. frozen compound butter and sauté until everything comes together; season to taste with salt and pepper. Do not overcook as the butter will separate if the pan is too hot.
Serve hot, garnished with sautéed lemon slices and 1 tbsp. each chopped parsley, Thai basil and Parmesan cheese. Enjoy this dish with a glass of pinot grigio.