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Preheat oven to 450°F with rack in middle.
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Cut a deep, wide pocket in each pork chop. Sprinkle half of sage into each pocket and stuff pockets with cheese and prosciutto. Pat chops dry and season with 1/4 tsp each of salt and pepper (total).
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Heat 1 Tbsp oil in a 12-inch ovenproof heavy skillet over medium-high heat until it shimmers. Cook chops until undersides are golden, about 2 minutes, then turn chops and transfer skillet to oven. Roast until cooked through, about 5 minutes.
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While chops cook, heat remaining Tbsp oil in a 5-qt pot over medium heat until it shimmers. Sauté garlic until pale golden, about 30 seconds. Add spinach and cook, covered, stirring occasionally, until wilted, about 3 minutes. Season with salt.
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Transfer chops to a platter. Add butter and lemon juice to hot skillet, stirring and scraping up brown bits, then pour sauce over pork.
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Serve pork with spinach.
