Heat the oven to 375°F (190°C). Lightly grease 8 wells of a standard muffin pan. Separate the crescent dough into 8 triangles and press one into each prepared well, covering the bottom and sides. Pinch any tears closed and leave the pointed edges at the rim.
Heat the olive oil in a large skillet over medium heat. Cook the onion for 2 to 3 minutes, then stir in the garlic for about 30 seconds. Add the ground beef and cook for 5 to 6 minutes, breaking it into small crumbles, until fully browned. Drain any pooled fat.
Stir in the finely chopped mushrooms. Cook for 3 to 4 minutes, or until the liquid they release has cooked away. Keep cooking a little longer if there is still liquid pooled in the skillet.
Add the salt, pepper, smoked paprika and thyme. Reduce the heat to low and stir in the softened cream cheese until melted and evenly mixed through the filling. Remove the skillet from the heat.
Divide the warm beef and mushroom filling evenly among the 8 dough cups. Leave the pastry edges visible. Sprinkle the shredded cheese evenly over the tops.
Bake on the center oven rack for 12 to 15 minutes, until the pastry is golden and baked through and the cheese is melted. If the pastry points brown before the bases are done, cover the pan loosely with foil and continue baking.
Rest the cups in the pan for 5 minutes. Gently loosen any stuck edges with a small silicone spatula and lift the cups out. The bottoms should be set and baked through. If a bottom still looks raw, return the cups to the pan and bake a little longer, covering the tops loosely with foil if needed. Serve warm.