In a large pot of salted water, cook pasta until al dente. Drain and set aside.

In a large saucepan, melt butter over medium heat. Sprinkle in the flour and cook mixture, stirring constantly, for a couple of minutes, until it begins to turn golden and is sandy-textured. Pour in milk in a thin, steady stream, whisking constantly, until sauce is smooth and uniform. Continue to cook until thick and bubbly. If the sauce gets too thick and gloopy, add a little more milk to thin it out.

Remove sauce from heat and stir in pesto, then fold in grated cheese. The residual heat should melt the cheese, but if it needs a little boost, return the sauce to low heat to melt it fully.

Add drained pasta to sauce and mix until the pasta is thoroughly coated. Serve hot, straight out of the pan, with an extra sprinkling of parmesan and, if you want to get fancy, garnish with basil leaves.