You can't. Firstly, as "jajko" is neuter (that's why you use "to", which is the neuter form of "this"), the adjective also has to match: "smaczne".
Secondly, you can only use the construction with "to" if on its both sides you have noun phrases. Here, on the right side you have only an adjective, so you can't use this construction.
As for double "to", it sounds perfectly possible, even if a little bit weird. "To zwierzę to tygrys" (This animal is a tiger). A normal sentence.
Is this usual way to say something "tastes good," or is there another common way?
For example, in English and German, we can say both: "the egg is yummy" ("tasty" isn't really said but is recognized)/"das Ei ist lecker" and "the egg tastes good"/"das Ei schmeckt gut" (or just "das Ei schmeckt").
We also use "dobrze smakuje" (I wouldn't rather say "smakuje dobrze" in this case but it is correct of course). "To jajko dobrze smakuje" (This egg tastes good). "Dobrze" might be replaced by "świetnie" (great). We may also say "smakuje komuś"/"komuś smakuje" ("komuś" should be replaced by a proper pronoun): "To jajko mi smakuje" (This egg tastes good to me).