Strip the leaves from the bottom 4 inches of each rosemary sprig. the sprigs will be your skewers. Finely chop 2-1/2 tsp. of the rosemary leaves and set aside (save the remaining leaves for another use).
Use a sharp wooden or metal skewer to poke holes through the sides of the scallops and the mushrooms. Carefully push the rosemary skewers through the holes, using 1 scallop and 1 mushroom per skewer. Don't worry if the mushrooms crack a little; they'll still stay on the skewer. Season all over with 1/4 tsp. salt and a few grinds of pepper. Put the kebabs on a baking sheet, mushroom caps stem side down. Cover the leafy ends of the sprigs with foil to prevent charring.
Mix the breadcrumbs with 1 Tbs. of the olive oil, 1-1/2 tsp. of the chopped rosemary, 1/2 tsp. salt, and a pinch of pepper.
Peel and chop the half garlic clove. Sprinkle it with 1/4 tsp. salt and mash to a paste with the side of a chef's knife. In a small bowl, whisk the garlic paste, crème fraîche, mustard, lemon juice, lemon zest, and the remaining 1 tsp. chopped rosemary. Season to taste with salt and pepper.
Position a rack 4 inches from the broiler and heat the broiler on high. Brush the mushroom caps (they should still be stem side down) and scallops with the remaining 2 Tbs. olive oil. Broil until beginning to brown and the scallops are almost cooked through, 3 to 5 minutes. Remove the pan from the oven and carefully flip the skewers. Fill the mushroom caps with 1 tsp. of the breadcrumbs. Spoon 1 Tbs. of the crème fraîche mixture per skewer into the mushrooms and over the scallops—it's fine if some slides off the scallops. Evenly mound the remaining breadcrumbs onto the mushrooms and scallops and pat gently to adhere. Broil until the breadcrumbs are nicely browned, 1 to 2 minutes more. Remove the foil and transfer to serving plates with a spatula.
The skewers can be threaded, seasoned, and refrigerated up to 2 hours before broiling.