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Blend butter and rosemary in processor.
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Gradually add oil and process until incorporated.
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Mix in Parmesan cheese.
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(Can be made 1 day ahead. Cover and refrigerate; bring to room temperature before continuing.)
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Mix in garlic.
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Cut the baguette in half lengthwise, then crosswise (4 pieces total).
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Score each piece diagonally 3/4-inch deep at 1 1/2-inch intervals.
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Prepare barbecue (medium-high heat) or preheat oven to 400°F
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Spread cheese mixture over cut sides of bread.
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If grilling, wrap each piece of bread loosely in foil.
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Grill in foil until bread is crusty and golden, about 8 minutes.
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If baking, place bread cut side up on baking sheet.
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Bake until bread is crisp and golden around edges, about 10 minutes.
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Serve bread warm.