In a medium frying pan over medium-high heat, cook bacon, turning as necessary, until browned but not completely crisp, 4 to 5 minutes. Transfer to paper towels to drain; when cool, finely chop.
In a bowl, mix chopped bacon with butter, 3 tbsp. minced shallots, 2 tsp. paprika, and thyme. Spoon across a sheet of plastic wrap and roll up into a 1 1/2-in.-thick log. Refrigerate at least 1 hour or up to 1 week. With a sharp knife, cut into slices about 1/4 in. thick to top oysters.
Note: Nutritional analysis is per oyster with 1 1/2 tsp. topping.