Preheat oven to 350°F. Season beef Ribeye Steak with salt and pepper, as desired. Place steak on grid over medium, ash-covered coals. Grill, uncovered 4 minutes on each side. Place steak in ovenproof, nonstick pan. Insert oven proof meat thermometer so tip is centered in thickest part of beef, not resting in fat or touching bone. Roast in 350°F oven 30 to 50 minutes.
Place tomatoes on aluminum foil-lined shallow baking sheet. Mix parmesan, garlic and 1 tablespoon basil in small bowl. Top each tomato half with 2 tablespoons Parmesan mixture. Add tomatoes to 350°F oven below steak 15 minutes before expected finish time.
Melt butter in large nonstick skillet over medium-high heat. Add zucchini, yellow squash and shallot slices; cook 8 to 10 minutes until tender and just starting to brown, stirring occasionally. Remove skillet from heat; stir in remaining 1 tablespoon basil. Season with salt and pepper, as desired. Keep warm.
Remove steaks from oven when meat thermometer registers 135°F for medium rare; 150°F for medium doneness. Transfer steaks to carving board; tent loosely with aluminum foil. Let stand 10 minutes. (Temperature will continue to rise about 10°F to reach 145°F for medium rare; 160°F for medium doneness.) Increase oven temperature to HIGH broil. Broil tomatoes 4 minutes until cheese begins to brown.
Serve steak with zucchini mixture and roasted tomatoes. Garnish with Italian Herb butter mixture and drizzle with Paprika-infused Oil, as desired.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.