Does the と quote the 面白い？
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Yes, this と is a quotative-と. と can be used without verbs like 思う and 考える (see this for example), but I think it's okay to think 笑う is directly taking the と-clause in this case. Either way, a literal translation of 私が心の底から面白いと笑って読める小説 would be "novels which I can read (while) smiling (while) thinking (it's) amusing from the bottom of my heart".