Iron concretion. Possibly siderite. FeCO3. Found in shale and very dense. That "something interesting in the middle" is a fossil or something that was in the water when deposition was taking place. If it were basalt you would have some kind of deformed contact boundary with the shale. Unless you are saying that the basaltic rock was placed in the shale after being formed which seems highly unlikely because the basalt would degrade in a weathering environment quite fast.